Find the general solution of the following equation?

Question

Find the general solution of the following equation?

y dy - 2 (yx+x) dx = 0

Please write the solution with full steps

Answer 1

Dividing by ydx we get; dy/dx = 2x(y + 1)/y; ydy/(y + 1) = 2xdx; ∫ydy/(y + 1) = ∫2xdx; ∫(1 - 1/(y + 1))dy = x² + C;

y - ln(1 + y) = x² + C. This is general solution in implicit form