Solve Second Order Differential Equation with Initial Conditions

I am trying to solve using the dsolve function:

D^2y/dt + p(dy/dt) + 2y = cos(w*t) with the conditions y(0) = 0 and y'(0) = 0

Assuming p = 0 and w cannot be 0.

Also how would I go about plotting the solutions of y(t) vs t for different values of w such as 0.5,0.6,0.7,0.8,0.9 and 0.95

How do I go about doing this?

Answer 1

[Star Strider]

Here you go:

syms y(t) p w t 
p = 0;
Deq = diff(y,2) + p*diff(y) + 2*y == cos(w*t);
Y = dsolve(Deq, diff(y(0)) == 0, y(0) == 0);
Y = simplify(Y, 'steps', 20);
Yfcn = matlabFunction(Y)

As for the plot, you will find the meshgrid function significantly helpful here. Read about it and surface and mesh in the documentation.

[Francisco Zapata]

How would I be able to edit the above code to accommodate for different values of w?

[Star Strider]

Use meshgrid to create your ‘t’ and ‘w’ matrices, then just give them to the ‘Yfcn’ anonymous function to create an output matrix, then plot the ‘t’ and ‘w’ matrices and the output matrix with surf or mesh.

[Francisco Zapata]

When I input your code into Matlab, it did not return a general solution? Am I doing something wrong?