web2.0calc
 
+0  
 

 differential equation bernoulli

+1
980
2
avatar+343 

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

1 Online Users

Top Users

avatar+129899 CPhill moderator
avatar+37153 ElectricPavlov
avatar+33661 Alan moderator
avatar+15000 asinus moderator
avatar+2511 GingerAle
avatar+2499 Solveit
avatar+1938 NotThatSmart
avatar+1557 parmen
avatar+1521 blackpanther
avatar+1455 kittykat
avatar+1310 learnmgcat

Sticky Topics