# Particular Integral

#### jpquinn91

I have $$\displaystyle d^2x/dt^2+2dx/dt-2=e^(-t)$$ and I have found CF = $$\displaystyle A+Be^(-2t)$$

I need to find the PI, usually I differentiate everything until you have a constant on the right or with an exp I would set $$\displaystyle x= e^(-t)v(t)$$ but neither seems to work, could someone help me with the method, thanks

#### ANDS!

Your guess for a particular solution is incorrect. What is the homogenous solution to: $$\displaystyle x''+2x'=e^{-t}+2$$?