ode45 with two 2nd order differential equation

Here I have two differential equations and I want to solve it using ode45

I am asked to convert the two 2nd order equations to 4 first-order equations which are suitable for ode45.

Answer 1

[Stephan]

https://de.mathworks.com/help/symbolic/odetovectorfield.html

Answer 2

[Steven Lord]

See the Higher-Order ODEs example on this documentation page and use the technique it illustrates to turn your system of two second order ODEs into a system of four first order ODEs.

Answer 3

[Pulkit Gahlot]

'first make the function file'

function xval =  pulfun(t,y)
%constant
u=0.012277471;
%define dy/dt
xval(1,1)=y(3);
xval(2,1)=y(4);
xval(3,1)=y(1)+2*y(4)-(1-u)*(y(1)+u)/((y(1)+u)^2+y(2)^2)^(1.5)-u*(y(1)-1+u)/((y(1)-1+u)^2+y(2)^2)^(1.5);
xval(4,1)=y(2)-2*y(3)-(1-u)*y(2)/((y(1)+u)^2+y(2)^2)^(1.5)-u*(y(2))/((y(1)-1+u)^2+y(2)^2)^(1.5);
end

'(then write a script file for use of ode45)'

y0=[0.994;0;0;-2.00158];
tspan=[10 40];

[tsol,ysol]=ode45(@(t,y) pulfun(t,y),tspan,y0);

plot(tsol,ysol)

i used my own terms. You can use your.

[darova]

Better be to separate and to make expressions clearer

Answer 4

[Stephane Sarrete]

Hello,

Please, I don't understand what the y (1), y (2), y (3) and y (4) represent in the function definition. Can be stupid question but I really do not understand. Thank you for helping me.

[Stephan]

Since 2 ode of order 2 are transformed into 4 ode of order 1, the 4 different entries of the y-vector represent the 4 four unknowns, to solve for.

Answer 5

[Stephane Sarrete]

Thanks so much for the help, I'll think about it.