Question

Find the general solution of the following differential equation:

(x²y - x²)dx + (xy² - y²)dy = 0

Answer 1

x²(y - 1)dx + y²(x - 1)dy = 0

\(\frac{x^2}{x-1}dx\) + \(\frac{y^2}{y-1}dy\) = 0

Add and subtract 1 in numerators ,

Splitting the terms,

(x + 1)dx + \(\frac{1}{(x-1)}dx\) + (y + 1)dy + \(\frac{1}{(y-1)}dy\)

Integrating,