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## Homework Statement

find a particular solutions for the given differentiable equation.

## Homework Equations

y''+5y'+6y=4-t^2

## The Attempt at a Solution

Because the right-hand side is a polynomial of degree 1, so I want to have a particular solution of the same form. It's like y=a(t^2)+b, but if so, I kinda stuck in the middle of calculation. 6a=-1 (this is fine) and 2a+10at+6b=4 (I want to take out t). i need to use this technique. Please help me find what's wrong here.

Thank you so much!