Hey all.

I am having a lot of trouble finding particular solutions.

I have three problems:

A) $\displaystyle y'' + y' = 6t^2$

B) $\displaystyle y'' - 4y = sin(2t)$

C) $\displaystyle y'' + 4y' + 5y = 5t + e^-t$

I am trying to find the particular solutions using the method of undetermined coefficients.

For A), I found the general solution to be

$\displaystyle Ce^-t + D$

and the particular solution to be

$\displaystyle (2t^4)/(2+t)$

For B), I found the general solution to be

$\displaystyle C + De^(4*t)$

and the particular solution to be

$\displaystyle (-1/8)sin(2t)$

For C), I found the general solution to be

$\displaystyle Ce^(-2*t+i*t) + De^(-2*t-i*t)$ (everything in the parenthesis after e is what e is raised to.

and the particular solution to be

$\displaystyle t + (1/2)e^(-t)$

None of these check out. I am flustered and frustrated with this and don't know what else to do. PLEASE HELP!!!

Thank you