tihs is going to sound like a stupid question, but how do i do it when the right side is like this?
x''+4x=1+t+sin(t) with initial conditions x(0)=0 and x'(0)=0
Next, you need to find the Particular Integral, by saying.
Comparing coefficients gives
So the solution to the PI is
The general solution to your equation is the sum of the solutions to the PI and the CF:
Plug in your initial conditions and you're done.