# How to solve a system of 3 ODE and a linear equation.

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Ricardo Mendes on 20 Feb 2021
How to solve a system of 3 ODE
dvdt=z;
dzdt=-v/(L0*C0)-z*R0/L0
dTempdt=R0*((C0*z)^2)/(m_ponte*Cp_Al)
and one linear equation: R=R0*(1+Alfa*(temp(i)-T0)) to consider the resistence variation with temperature instead of constant resistence R0?
F=@(t, v, z, temp) [z; -v/(L0*C0)-z*R0/L0; R0*((C0*z)^2)/(m_ponte*Cp)];
v(1)=-20000;
z(1)=0;
temp(1)=298;
t(1)=0;
for i=1:N
k1 = h*F(t(i), v(i), z(i), temp(i));
k2 = h*F(t(i)+h/2, v(i)+k1(1)/2, z(i)+k1(2)/2, temp(i)+k1(3)/2);
k3 = h*F(t(i)+h/2, v(i)+k2(1)/2, z(i)+k2(2)/2, temp(i)+k2(3)/2);
k4 = h*F(t(i)+h, v(i)+k3(1), z(i)+k3(2), temp(i)+k3(3));
v(i+1) = v(i) + (1/6)*(k1(1)+2*k2(1)+2*k3(1)+k4(1));
z(i+1) = z(i) + (1/6)*(k1(2)+2*k2(2)+2*k3(2)+k4(2));
temp(i+1) = temp(i) + (1/6)*(k1(3)+2*k2(3)+2*k3(3)+k4(3));
end

Shadaab Siddiqie on 23 Feb 2021
From my understanding you want to solve an 3rd degree ODE equations. You can go through solve ODE, symbolic variables and expressions and also dsolve for more information.

R2018b

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