Initial Value Problem using method of undetermined coefficients

y'' + y' - 6y = 3te^(2t)

with initial conditions:

y(0) = 3

y'(0) = 5

Help please! I have a start...

The associated auxilery equations is

r^2 + r - 6 = 0

r = -3 and r = 2

I think r is a single root since looking at the equations ay'' + by' + cy = Ct^(m)e^(rt)

r = 2.

so I think s = 1 in the following equation

so yp(t) = t^(s)(Am*t^(m) + A1t _ A0)e^(rt) is the equation used for method of undetermined coefficients

Re: Initial Value Problem using method of undetermined coefficients