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

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- Feb 4th 2009, 08:58 PMgambler84solving the differential equation
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 - Feb 5th 2009, 12:04 AMGrandadDifferential equation
Hello gambler84Since you talk about the right-hand-side, I assume you know how to solve the Complementary Function to get

Next, you need to find the Particular Integral, by saying.

Let

Then

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.

Grandad