It must be easy but needing help w/ x*dy/dx = x^2 + y^2 + y

[davemath]

It must be quite easy but I don't know why I cannot solve this:

x*dy/dx = x^2 + y^2 + y

Thank you for your helps in advance.

 

[royhaas]

Subtract \(\displaystyle y\) from both sides and divide by \(\displaystyle x^2\).

 

[davemath]

Hi,

After that, at least I need one more step!!
What I guess is d(y/x) = dy/x=y/x^2*dx

 

[davemath]

Hi,

I think I know now.....
Thanks a lot for your help!

 

[davemath]

No....I can still not solve the problem, can you help?

 

[royhaas]

\(\displaystyle (y/x)' = 1 + (y/x)^2\).

 

[davemath]

Yes, I have also reached du/dx=1+u^2, but it looks not like Bernoulli equation......

 

[royhaas]

\(\displaystyle du/(1+u^2) = dx\).

 

[davemath]

Hahaha, you must believe that I am stupid!
Thanks a lot for your help.