Answer to Question #249991 in Differential Equations for Anita

Question

Solve by method of separation of variable Î ”

Answer 1

Solve by method of separation of variable

$ydx-xdy=0$

Solution:

$ydx-xdy=0 \\ \Rightarrow ydx=xdy \\ \Rightarrow \dfrac {dx}x=\dfrac {dy}y$

On integrating both sides,

$\ln x+\ln C=\ln y \\\Rightarrow \ln Cx=\ln y \\\Rightarrow Cx=y$