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**snaes** Hi, i read over this post i think i know how to find a "general solution" for this probelm. Its actually a specific case for this problem, but it'll help you find an integrating factor in the form $\displaystyle x^ay^b$. where "a" and "b" are constants.

Get equation in exact form:

$\displaystyle (M)dx+(N)dy=0$

$\displaystyle (-y)dx+(3x-y)dy=0$

Make this fraction =1

$\displaystyle \dfrac{M_y-N_x}{N\dfrac{a}{x}-M\dfrac{b}{y}}=1$

By making "a" and "b" appropriot values this should make the fraction 1. Thereby giving you the values of "a" and "b"to fill in the integrating factor $\displaystyle x^ay^b$.

This should make the equation turn into an "exact differential equation"

Hope this helps!

*Note: I havent tried this for your specific problem, but this is the solution my professor has taught us and has worked for me on other problems.