solving differential equation and plotting them

28 May 2022
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Updated 29 May 2022
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greetings im trying to plot these differnatial equations but all i have is empty plots
Omega= 4;
Gamma2=4;
CapitalOmega = 2;
CapitalDelta1 = 0.8;
CapitalDelta2 = CapitalDelta1-Omega;
CapitalOmega2= 2*CapitalOmega;
CapitalGamma1=0.5+(i*CapitalDelta1);
CapitalGamma2=0.5*Gamma2+ (i*CapitalDelta2);
p=1;
syms x(t) y(t) z(t) f(t)
odex=diff(x,t)==-CapitalGamma1*x-0.5*p*sqrt(Gamma2)*y+CapitalOmega*z;
odey=diff(y,t)==-CapitalGamma2*x-0.5*p*sqrt(Gamma2)*x+CapitalOmega2*z;
odez=diff(z,t)==-CapitalOmega*x-CapitalOmega2*y;
condx= x(0) == 1;
xSol(t) = dsolve(odex,condx);
xSol=simplify(xSol)
condy= y(0) == 0;
ySol(t) = dsolve(odey,condy);
ySol=simplify(ySol)
condz= z(0) == 0;
zSol(t) = dsolve(odez,condz);
zSol=simplify(zSol)
odef=diff(f,t)== -x-y;
fSol(t) = dsolve(odef);
fSol=simplify(fSol)
fsol=subs(fSol,t,0.6)
fplot([fsol xSol ySol zSol])

7 Comments
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Torsten
Torsten on 28 May 2022
You mustn't solve the differential equations one after the other, but all in one.
Faisal Al-Wazir
Faisal Al-Wazir on 28 May 2022
yes i tried but with no luck,i added this codes to my code
conds =
x(0) == 1
y(0) == 0
z(0) == 0
>> odes=[odex;odey;odez]
odes(t) =
diff(x(t), t) == 2*z(t) - y(t) - x(t)*(1/2 + 4i/5)
diff(y(t), t) == 4*z(t) - x(t)*(3 - 16i/5)
diff(z(t), t) == - 2*x(t) - 4*y(t)
>> [xSol(t),ySol(t),zSol(t)] = dsolve(odes,conds)
xSol(t) =
(exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(300 + 480i) + 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) + 3^(1/2)*(880 - 5139i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*900i - (5139 + 880i)))/(1800*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*((12953/242496 + 14191i/202080)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(75/6736 + 35i/3368) + ((571/200 + 22i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)/2 + (3^(1/2)*((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3))*1i)/2 - (1/6 + 4i/15))^2*(75/1684 + 35i/842) - 3^(1/2)*((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3))*(35/3368 - 75i/6736) + (18037/20208 + 8305i/10104))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(828000 + 832500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(16689525 - 11741640i) + 405000*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3) + 3^(1/2)*(23151600 + 1309709i) + (1843511/30000 - 229103i/675)^(1/2)*(2497500 - 2484000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3913880 + 5563175i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*135000i + (3929127 - 69454800i))*(1/3 + 2i/3))/(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i)) + (2*exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(150 + 240i) - 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) + (5139 + 880i)))/(900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*((- 12953/121248 - 14191i/101040)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(75/3368 + 35i/1684) + ((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + (1/6 + 4i/15))^2*(75/1684 + 35i/842) + (18037/20208 + 8305i/10104))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(100431719766000 - 125302533408000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(617277561988480 + 695983152529460i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(134912787051175 + 19930429504100i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(128158529940000 + 68058174780000i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(15447422250000 + 41778342000000i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(236925000000 - 801900000000i) + 3^(1/2)*(391863722188 - 3282080284324724i) + (1843511/30000 - 229103i/675)^(1/2)*(125302533408000 + 100431719766000i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3990838803534380 + 9148072702738810i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(19930429504100 - 134912787051175i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(28763284140000 - 142285399470000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(41778342000000 - 15447422250000i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(801900000000 + 236925000000i) + (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(47070085185000 - 1079373780000i) - (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(3845475000000 + 6658200000000i) + 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(115053136560000 - 569141597880000i) - 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6138180000000 - 3069090000000i) + 3282080284324724 + 391863722188i))/((3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(765000 + 1345500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(25292415 - 9157650i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6075000 + 5670000i) - 3^(1/2)*(50036022 - 47750305i) + (1843511/30000 - 229103i/675)^(1/2)*(4036500 - 2295000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3052550 + 8430805i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1890000 - 2025000i) + 143250915 + 150108066i)) + (4*exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(300 + 480i) + 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) - 3^(1/2)*(880 - 5139i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*900i - (5139 + 880i)))/(1800*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*((12953/242496 + 14191i/202080)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(75/6736 + 35i/3368) + ((- 571/200 - 22i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)/2 + (3^(1/2)*((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3))*1i)/2 + (1/6 + 4i/15))^2*(75/1684 + 35i/842) + 3^(1/2)*((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3))*(35/3368 - 75i/6736) + (18037/20208 + 8305i/10104))*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(308638780994240 + 347991576264730i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(134912787051175 + 19930429504100i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(64079264970000 + 34029087390000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(15447422250000 + 41778342000000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(236925000000 - 801900000000i) - (1843511/30000 - 229103i/675)^(1/2)*(125302533408000 + 100431719766000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(1995419401767190 + 4574036351369405i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(14381642070000 - 71142699735000i) + (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(23535042592500 - 539686890000i) - (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1922737500000 + 3329100000000i) - 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(57526568280000 - 284570798940000i) + 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(3069090000000 - 1534545000000i) - 3282080284324724 - 391863722188i))/((3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(765000 + 1345500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(25292415 - 9157650i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6075000 + 5670000i) - 3^(1/2)*(50036022 - 47750305i) + (1843511/30000 - 229103i/675)^(1/2)*(4036500 - 2295000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3052550 + 8430805i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1890000 - 2025000i) + 143250915 + 150108066i))
ySol(t) =
(exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(300 + 480i) + 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) + 3^(1/2)*(880 - 5139i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*900i - (5139 + 880i)))/(1800*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*((8977901/12124800 + 38153i/242496)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(1759/13472 + 35i/6736) + ((571/200 + 22i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)/2 + (3^(1/2)*((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3))*1i)/2 - (1/6 + 4i/15))^2*(75/3368 + 35i/1684) - 3^(1/2)*((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3))*(35/6736 - 1759i/13472) + (5451/13472 + 34789i/101040))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(828000 + 832500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(16689525 - 11741640i) + 405000*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3) + 3^(1/2)*(23151600 + 1309709i) + (1843511/30000 - 229103i/675)^(1/2)*(2497500 - 2484000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3913880 + 5563175i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*135000i + (3929127 - 69454800i))*(- 1/3 - 2i/3))/(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i)) - (2*exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(150 + 240i) - 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) + (5139 + 880i)))/(900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*((- 8977901/6062400 - 38153i/121248)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(1759/6736 + 35i/3368) + ((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + (1/6 + 4i/15))^2*(75/3368 + 35i/1684) + (5451/13472 + 34789i/101040))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(100431719766000 - 125302533408000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(617277561988480 + 695983152529460i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(134912787051175 + 19930429504100i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(128158529940000 + 68058174780000i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(15447422250000 + 41778342000000i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(236925000000 - 801900000000i) + 3^(1/2)*(391863722188 - 3282080284324724i) + (1843511/30000 - 229103i/675)^(1/2)*(125302533408000 + 100431719766000i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3990838803534380 + 9148072702738810i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(19930429504100 - 134912787051175i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(28763284140000 - 142285399470000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(41778342000000 - 15447422250000i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(801900000000 + 236925000000i) + (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(47070085185000 - 1079373780000i) - (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(3845475000000 + 6658200000000i) + 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(115053136560000 - 569141597880000i) - 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6138180000000 - 3069090000000i) + 3282080284324724 + 391863722188i))/((3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(765000 + 1345500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(25292415 - 9157650i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6075000 + 5670000i) - 3^(1/2)*(50036022 - 47750305i) + (1843511/30000 - 229103i/675)^(1/2)*(4036500 - 2295000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3052550 + 8430805i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1890000 - 2025000i) + 143250915 + 150108066i)) - (4*exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(300 + 480i) + 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) - 3^(1/2)*(880 - 5139i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*900i - (5139 + 880i)))/(1800*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*((8977901/12124800 + 38153i/242496)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(1759/13472 + 35i/6736) + ((- 571/200 - 22i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)/2 + (3^(1/2)*((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3))*1i)/2 + (1/6 + 4i/15))^2*(75/3368 + 35i/1684) + 3^(1/2)*((571/100 + 44i/45)/((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3))*(35/6736 - 1759i/13472) + (5451/13472 + 34789i/101040))*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(308638780994240 + 347991576264730i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(134912787051175 + 19930429504100i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(64079264970000 + 34029087390000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(15447422250000 + 41778342000000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(236925000000 - 801900000000i) - (1843511/30000 - 229103i/675)^(1/2)*(125302533408000 + 100431719766000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(1995419401767190 + 4574036351369405i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(14381642070000 - 71142699735000i) + (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(23535042592500 - 539686890000i) - (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1922737500000 + 3329100000000i) - 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(57526568280000 - 284570798940000i) + 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(3069090000000 - 1534545000000i) - 3282080284324724 - 391863722188i))/((3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(765000 + 1345500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(25292415 - 9157650i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6075000 + 5670000i) - 3^(1/2)*(50036022 - 47750305i) + (1843511/30000 - 229103i/675)^(1/2)*(4036500 - 2295000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3052550 + 8430805i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1890000 - 2025000i) + 143250915 + 150108066i))
zSol(t) =
(exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(300 + 480i) + 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) + 3^(1/2)*(880 - 5139i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*900i - (5139 + 880i)))/(1800*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(828000 + 832500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(16689525 - 11741640i) + 405000*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3) + 3^(1/2)*(23151600 + 1309709i) + (1843511/30000 - 229103i/675)^(1/2)*(2497500 - 2484000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3913880 + 5563175i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*135000i + (3929127 - 69454800i))*(1/3 + 2i/3))/(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i)) + (4*exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(300 + 480i) + 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) - 3^(1/2)*(880 - 5139i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*900i - (5139 + 880i)))/(1800*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(308638780994240 + 347991576264730i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(134912787051175 + 19930429504100i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(64079264970000 + 34029087390000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(15447422250000 + 41778342000000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(236925000000 - 801900000000i) - (1843511/30000 - 229103i/675)^(1/2)*(125302533408000 + 100431719766000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(1995419401767190 + 4574036351369405i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(14381642070000 - 71142699735000i) + (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(23535042592500 - 539686890000i) - (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1922737500000 + 3329100000000i) - 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(57526568280000 - 284570798940000i) + 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(3069090000000 - 1534545000000i) - 3282080284324724 - 391863722188i))/((3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(765000 + 1345500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(25292415 - 9157650i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6075000 + 5670000i) - 3^(1/2)*(50036022 - 47750305i) + (1843511/30000 - 229103i/675)^(1/2)*(4036500 - 2295000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3052550 + 8430805i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1890000 - 2025000i) + 143250915 + 150108066i)) + (2*exp(-(t*(((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(150 + 240i) - 900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3) + (5139 + 880i)))/(900*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)))*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(100431719766000 - 125302533408000i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(617277561988480 + 695983152529460i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(134912787051175 + 19930429504100i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(128158529940000 + 68058174780000i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(15447422250000 + 41778342000000i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(236925000000 - 801900000000i) + 3^(1/2)*(391863722188 - 3282080284324724i) + (1843511/30000 - 229103i/675)^(1/2)*(125302533408000 + 100431719766000i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3990838803534380 + 9148072702738810i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(2/3)*(19930429504100 - 134912787051175i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(28763284140000 - 142285399470000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(5/3)*(41778342000000 - 15447422250000i) - 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(8/3)*(801900000000 + 236925000000i) + (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(47070085185000 - 1079373780000i) - (1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(3845475000000 + 6658200000000i) + 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(115053136560000 - 569141597880000i) - 3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6138180000000 - 3069090000000i) + 3282080284324724 + 391863722188i))/((3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(2530420 - 12517410i) - 3^(1/2)*(58458002 + 199873999i))*(3^(1/2)*(1843511/30000 - 229103i/675)^(1/2)*(765000 + 1345500i) - ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(25292415 - 9157650i) + ((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(6075000 + 5670000i) - 3^(1/2)*(50036022 - 47750305i) + (1843511/30000 - 229103i/675)^(1/2)*(4036500 - 2295000i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(1/3)*(3052550 + 8430805i) + 3^(1/2)*((1843511/30000 - 229103i/675)^(1/2) + 70313/5400 - 56261i/3375)^(4/3)*(1890000 - 2025000i) + 143250915 + 150108066i))
Torsten
Torsten on 29 May 2022
And what is the problem ? Matlab returned the solutions for x, y and z.
Torsten
Torsten on 29 May 2022
Edited: Torsten on 29 May 2022
fplot(xSol)
does not work ?
Faisal Al-Wazir
Faisal Al-Wazir on 29 May 2022
yes it doesn't work it gives an empty plot
Torsten
Torsten on 29 May 2022
Ah, I see: xSol is complex-valued.
So you have to use
fplot(real(xSol)), fplot(imag(xSol)), fplot(abs(xSol))
to plot instead of
fplot(xSol)
If this doesn't work either, use
xSol = matlabFunction(xSol);
t = 0:0.01:3;
plot(t,abs(xSol(t))) % e.g.

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Asked:

Faisal Al-Wazir
Faisal Al-Wazir
on 28 May 2022

Commented:

Torsten
Torsten
on 29 May 2022

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