Question

Find the particular solution of the differential equation x(1 + y²) dx-y(1 + x²) dy = 0, given that y = 1 when x = 0.

Answer 1

\(\cfrac{2xdx}{1+x^2}\) - \(\cfrac{2ydy}{1+y^2}\) = 0

⇒ \(\cfrac{log(1+x^2)}{1+y^2}\) = 0