Question

Find the general solution of the differential equation ydx -(x+2y)dy=0

Answer 1

Final Answer :
$\frac{x}{y} = 2 ln( |y| ) + c$

Steps :
1) We have,
$y \: dx - (x + 2y) \: dy = 0 \\ = > y \: dx \: - x \: dy \: - 2y \: dy \: = 0 \\ = > {y}^{2} d( \frac{x}{y} ) - 2y \: dy = 0$

2) Assuming y is not equal to 0.
Then,
$d (\frac{x}{y} ) = 2 \frac{dy}{y}$
Integrating both sides.
$= > \frac{x}{y} = 2 ln( |y| ) + c \:$
This is required Implicit equation.