Question

Solve the differential equation xdx + ydy + (xdy - ydx)/(x² + y²) = 0

Answer 1

We know that 

d(x² + y²) = 2(xdx + ydy)

Therefore, the equation becomes

1/2d(x² + y²) + dtan^-1(y/x) = 0 (exact equation)

On integrating, we get

Therefore, y = xtan((c - x² - y²)/2).