Solving a Bernoulli differential equation

[Boxiom]

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!

 

[JJacquelin]

Hi !
see attachment

 

[Boxiom]

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:

What exactly did they do to simplify it like that?

 

[JJacquelin]

Where is the problem after the correction of sign ?