# Differential Equations Variation of Params Problems

## Homework Statement

$$t^{2}$$ * y'' - 2y = $$3t^{2}$$ - 1

$$y_{1}$$ = t$$^{2}$$

$$y_{2}$$ = 1/t

## Homework Equations

Variation of Params forumla
wronskian det

## The Attempt at a Solution

W = t^2 * -t^-2 -[1/t * 2t] = -3

Y = -t^2 * Integral[ (-1/3)(1/t)(3t^2 -1)] + 1/t * Integral[(-1/3)(t^2)(3t^2 -1)]

I get an answer that is not correct so I guess I set this part up wrong somehow anyone see the error?

My answer: Y = 3/10*t^4 - t^2 * ln|t|/3

Correct Answer: Y = t^2*ln|t| + 1/2

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