Variation of Parameters problem

[pergradus]

Homework Statement

Find a particular solution by method of variation of parameters:

t²y'' - 2y = 3t² - 1

given:

y₁ = t²
y₂ = t^-1

Homework Equations

The Attempt at a Solution

I get $$Y(t) = t^2ln(t) - \frac{1}{3}t^2 + \frac{1}{2}$$

The book gives $$Y(t) = t^2ln(t) + \frac{1}{2}$$

I don't understand why they are off by the 1 term?

 

[HallsofIvy]

The only thing I can tell you is that they aren't off by one term- you are!

And since you don't show any work, we can't say why you are. I suspect you have an error in your second integral.

 

[pergradus]

The only thing I can tell you is that they aren't off by one term- you are!

And since you don't show any work, we can't say why you are. I suspect you have an error in your second integral.

By "they" I was referring to the the two answers - mine and theirs.

And I made no mistakes in the integration - check my work if you want. This is the THIRD time I've done this problem and I get the same answer.

It will take me hours to type this in LaTex so please just look at picture I uploaded. The -1/3t² term just doesn't go away.