Thread: 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.

Thank you for your assistance.

Originally Posted by taurine330

Need to find the general solution q(t) of

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

solve the homogeneous.

the characteristic equation is so we have equal roots and the solution is

see my second link to find the particular solution.