Homework Help, Solving particular solution for ODE (a)Find the particular solution to 
$y''+2y'+y=\frac{5.5e^{-t}}{t^2+1}$
my question is how to find particular solution when right hand side is negative power
(b)$x^2y''+19xy'+81y=x^7$
by Euler's equation, let $t=lnx$
we have $\frac{d^2y}{dt^2}+18\frac{dy}{dt}+81y$ but this is only the case when its homogeneous equation. I don't know how the right hand side would be after the substitution

Hint:
$$y'' + 2y' + y = e^{-t}(y e^{t})'' = \frac{5.5e^{-t}}{(1+t^2)}$$
Now multiply both sides by $e^{t}$ and integrate twice. Two useful integrals are: $$\int \frac{dt}{1+t^2} = \arctan(t)$$
$$\int\arctan(t)dt = t\arctan(t) - \frac{1}{2}\log(1+t^2)$$
