Solve a non linear differential equation

Hello,

I have an equation like: Az"+Bz'+Cz'sin(Dz+E)+Fz=G with A,B,C,D,E,F,G are constant, and initial conditions known.

I have to solve it using Matlab, but I really don't know how to do, even after looking for information on Internet, could you help me or tell me what function I have to use?

Thank you in advance,

Romain CHAUDET

Answer 1

[Star Strider]

You can find the technique of creating a companion matrix from a differential equation in most differential equation textbooks, so I will spare you the discussion here.

[A,B,C,D,E,F,G] = deal(3,5,7,11,13,17,19);
odez = @(t,z) [z(2); (-B.*z(2)-C.*z(2).*sin(D*z(1)+E)-F.*z(1)+G)./A];

ts = linspace(1, 10, 250);
[t,z] = ode45(odez, ts, [0; 0]);

figure(1)
plot(t, z)
grid
legend('z(t)', 'z’(t)')

[Romain Chaudet]

Thank you very much for your help, this worked well!

Romain CHAUDET

[Star Strider]

My pleasure!