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## Homework Statement

[tex]y'' = t^2[/tex]

## The Attempt at a Solution

The general solution to the homogenous diff equation is [tex]y(t)= C1 + tC2[/tex] i beliee. The particular solution is where i am having trouble.

the guess is of the form [tex]\alpha t^2 + \beta t + \gamma[/tex] ... but taking 2 deriatives leads to just [tex]2\alpha = t^2[/tex] ... this can only be zero if [tex]\alpha = \frac{t^2}{2}[/tex] but this is something i haven't encountered as the constants are usually numeric values... and what about the rest of constants of beta and gamma?