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Math Separation Of Variables Sample Problem

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I have no idea how to start this problem.

dN/dt + N = Nte^t+2

So far I have, dN/dt = Nte^t+2 - N
where do I go from there.

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Solution Summary

The separation of variables for a sample problem are provided.

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I provide a way to solve this kind of equations. But for this problem, the solution is very complicated and it includes an integral which I can't find a ...

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