Variation of parameters. unsure why my solution differs from professor's

[fufufu]

Homework Statement

what is general solution of 2y'' - 3y' + y = ((t^2) + 1)e^t

Homework Equations

my particular solution is: (e^t) ((2/3)(t^3) + 6t -4))
prof particular solution is: ((1/3)(t^3)(e^t)) - 2(t^3)(e^t) + 9(te^t)

The Attempt at a Solution

here is how i solved , i hope this is ok to post link tp pdf..its faster than typing this all out..
https://docs.google.com/open?id=0BwJqUg33PgREQTFaejBCUkRRWlNfRW9maU1oaDNYQQ

thanks for any help/advice/hints

 

[ehild]

You can check if your solution is correct by substituting back into the original equation. ehild

 

[ehild]

As the coefficient of y'' is not 1 in the original equation, you have to divide the right-hand side by 2 when calculating u' and v'.

I think you did not copy your professor's solution correctly. It has to be
(1/3 t³-2t²+9t)e^t.

ehild