# Math Help - Differential eqn

1. ## Differential eqn

find the general solution of

i know this is a first order non linear differential eqn

but how to solve this equation

i divided by xy tried to make this exact and then find the integrating factor but i am unable to do so

help

2. ## Re: Differential eqn

Originally Posted by prasum
find the general solution of
i know this is a first order non linear differential eqn
but how to solve this equation
i divided by xy tried to make this exact and then find the integrating factor but i am unable to do so
help
I suppose that it is a textbook exercice. So, it cannot be as difficult as the solving of the above ODE.
This draw to think that there is a typo in the equation.
For example, the corrected ODE might be as shown below. Then the integrating factor would be 1/(xy)^4

3. ## Re: Differential eqn

There is no typo in the problem

4. ## Re: Differential eqn

Originally Posted by prasum
find the general solution of

i know this is a first order non linear differential eqn

but how to solve this equation

i divided by xy tried to make this exact and then find the integrating factor but i am unable to do so

help
It isn't exact, I can't find an integrating factor, and it's not homogeneous. I'm starting to side with "JJ". You may have transcribed it correctly, but I'm guessing the book itself might have a typo.

-Dan

5. ## Re: Differential eqn

i divided it by xy then separated dx and dy terms to get
ydx+xdy+2xy^3dx-x^2ydy=0
then
d(xy)+i can make this part exact by calculating the integrating factor in terms of y and then solving it

6. ## Re: Differential eqn

Originally Posted by prasum
i divided it by xy then separated dx and dy terms to get
ydx+xdy+2xy^3dx-x^2ydy=0
then
d(xy)+i can make this part exact by calculating the integrating factor in terms of y and then solving it