Question

Solve : (x + log y)dy + ydx = 0

Answer 1

Given differential equation can be written as

(xdy + ydx) + log y. dy = 0

or, d(xy) + log y dy = 0

Integrating we get

∫d(xy) + ∫log y dy = c

xy + y log y - y = c

which is the required solution.