Particular Integral

Oct 2009
48
0
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
 
Jul 2009
593
165
Your guess for a particular solution is incorrect. What is the homogenous solution to: \(\displaystyle x''+2x'=e^{-t}+2\)?