MATLAB: Solving Complex Coupled Differential Equations

differential equationsnonlinear

Hello,
My question is as follows. Say we have a set of coupled differential equations, such as
y'' = x' + y' + cos(y) and x'' = y'^2 + tan(y).
How would I go about implementing this with the regular ODE software? I understand how to solve coupled differential equations, and normal ODEs, but I've never had to deal with coupled differential equations with derivatives on both side.
Cheers

Best Answer

These are relatively straightforward. To use the ODE solvers however, they have to use the same variable, that requires that you keep track of what is x and what is y:
couplode = @(t,y) [y(2); y(4)^2 + tan(y(3)); y(4); cos(y(3)) + y(2) + y(4)];
[t,y] = ode45(couplode, [0 0.49*pi], [1;1;1;1]*1E-8); 
figure(1)
plot(t, y)
grid
str = {'$$ \dot{y} $$', '$$ y $$', '$$ \dot{x} $$', '$$ x $$'};
legend(str, 'Interpreter','latex', 'Location','NW')
produces this interesting plot:
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