Solving a Bernoulli differential equation

Boxiom
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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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Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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