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# Differential Equations and Variation of Parameters

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Solve t^2y''+ty'-y=2t^2 sin t t not equal to zero

Use method of variation of parameters
Solve &#8747;t^2 sin t dt= -t^2 cos t + 2t sin t +2 cos t

https://brainmass.com/math/calculus-and-analysis/differential-equations-variation-parameters-40762

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I assume we could use the integral you provided as is.

To solve

One must first solve the associated homogenous equation

This equation can be solved using a "guess":

Substituting ...

#### Solution Summary

An ODE and an integral are solved. The solution is detailed and well presented.

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