Thread: Help on a differential equation

1. Help on a differential equation

Need to find the general solution q(t) of

q''+ 6q'+ 9q = (t^2)*(e^(-3t))

I think it goes of finding solution of the form P(t)*e^(-3t) with P polynomial of degree 4.

But not totally sure how to continue.

the characteristic equation is $r^2+6r+9=0,$ so we have equal roots and the solution is $q_h(t)=c_1e^{-3t}+c_2te^{-3t}.$