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 differential equation bernoulli

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I need a little dit help

In this equation

\(y'+x+y+1=(x+y)^2{e}^{2x}\)

I stuck at this point:

\({y}^{-2}y'+{y}^{-1}(1-2x{e}^{x})=({e}^{2x}+\frac{(x^2{e}^{2x}+x+1)}{y^2})\)  But its 100% false because its not bernulli at this point,I need an other way,any help?

I need only the other step don't solve all the differential equation

Thank you!

 Oct 20, 2019
edited by Dimitristhym  Oct 20, 2019
edited by Dimitristhym  Oct 20, 2019
edited by Dimitristhym  Oct 20, 2019
edited by Dimitristhym  Oct 20, 2019

2+0 Answers

 #1
avatar+397 
+3

Your first step should be the substitution z = x + y.

That gets you the equation

\(\displaystyle \frac{dz}{dx}+ z=z^{2}e^{2x}. \)

Now use the usual Bernoulli substitution.

 Oct 21, 2019
 #2
avatar+33661 
+3

I would substitute \(z=(x+y)e^x \)

 

Then you get \(\frac{dz}{dx}=z^2e^x\)  which is easy to solve by separation of variables.

 Oct 21, 2019

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