Reduce Order (diff eq)

[SOLVED] Reduce Order (diff eq)

nevermind i got it, cliffsnotes ftw

Homework Statement

Solve the differential equation using the reduction of order method.
$$t^2 y'' - 4ty' + 6y = 0$$
$$t > 0$$
$$y_1 (t) = t^2$$

The Attempt at a Solution

Well The first thing I do is
$$y(t) = v(t) t^2$$
Then I find y' and y'' and plug into the original diff eq and get
$$t^4 v'' = 0$$
Which I'll assume is correct.

But now I'm really not sure what to do with that. I could do integration by parts? but that doesn't seem to lead anywhere. How do I get from there to t^3 (the other solution)?

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