How to solve a differential equation with MATLAB

Question

i have a problem. that is :

y"^2 + 2*y'+ 3*y = sin(x), y'(0)=0, y(0)=1

I want solve this problem with MATLAB but I can't.

Can you help me ?

Answer 1

First, you have to reduce the order. Let z = y' => z' = y"

Your ODE then becomes

z' = sqrt(-2*z - 3*y + sin(x)), with z(0) = 0
y' = z, with y(0) = 1

You can now write a function in MATLAB to represent this ODE: (where M = [ z y ]')

function dMdx = odefunc(x,M)
    z = M(1);
    y = M(2);
    dMdx(1) = sqrt(-2*z - 3*y + sin(x));
    dMdx(2) = z;
end

You can then call this function as follows:

M0 = [ 0 1 ];   % Initial values of ODE
tfinal = 12;     % Final integration time
[x,M] = ode45(@odefunc,[0 tfinal],M0)   % Integration using the RK-45 algorithm