Solve the following initial value problemy′′ + 9y = 3 cos(3x), y(0) = 0, y′(0) = 0 and write the final solution using real valued functions. Sketch the graph of the solution in a x-y diagram.
Can someone help me solve this?
This is what i done so far
y′′ + 9y - 3 cos(3x)= 0
z^2 +9z -3 cos(3x)= 0
z(z+6) + 3(z-cos(3x))=0
Now im really stuck on what to do. Please help. Thanks.
Fist we need to solve the homogenious equation
So this gives us the complimentry solution
Now we need to find a particualr solution. There are a few different ways to do this, but here is one way.
so the final solution is
Now using the intial conditions we get
taking the derivative we get
using the 2nd ic we get