Answer to Question #145228 in Differential Equations for Nikhil Singh

Question

Solve
(2√xy -y)dx- xdy=0

Answer 1

Given $(2\sqrt{x}y - y)dx - xdy =0$

Using seperation of variables method we have that:

$y(2\sqrt{x} - 1)dx = xdy$

Rearranging the equation we have that:

$\frac{(2\sqrt{x} - 1)dx}{x} = \frac{dy}{y}$

Taking the integral of both sides we have that:

$4\sqrt{x} - Inx + c = Iny$

which is the general solution