Solving a Bernoulli differential equation

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SUMMARY

The discussion centers on solving a Bernoulli differential equation, where the user initially miscalculated the solution due to a sign error. The correct form of the solution involves the term -te^-t, which differs from the user's initial calculation of te^-t. The user references Wolfram Alpha for verification but remains confused about the simplification process and the discrepancy with the textbook answer.

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Hello!

I'm stuck at the moment with this differential equation. I've been trying to use the method for solving these equations, but my answer is not correct according to my book. Could anyone please explain what I'm doing wrong? Thanks!

WkjWSEE.png
 
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Hi !
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Hi and thanks for your reply =)

A stupid mistake from my side, I changed it up and the only difference in the answer is that te^-t is now -te^-t. Still, the book doesn't agree with me unless they have the answer on some weird form. I also checked wolfram, they gave me this answer:

WJ6eFxI.gif


What exactly did they do to simplify it like that?
 
Where is the problem after the correction of sign ?
 

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