Is reduction of order a simpler method for solving this integral?

[VonWeber]

The problem has ty'' - (1 + t)y' + y = (t^2)e^2t

y1 = 1 + t

Solve by reduction of order

When I solve by variation of parameters I get:

y = .5te^2t - .5e^2t + ce^t + d(1 + t)

But solving with reduction of order gives very difficult integrals

 

[VonWeber]

Well I should have seen this one

(ue^u - e^u)/u^2 is a quotient rule.