Question

Solution of the differential equation ydx -xdy=xydx

Answer 1

int(y/xy)dx-int(x/xy)dy=intdx
Or, lnx-lny=x+k
or, ln(x/y)=x+k

Answer 2

Answer :

$\frac{x}{y}=e^{x+c}$

Step by step explanation :

Given : Differential equation $ydx -xdy=xydx$

To find : The solution of differential equation

Solution :

$ydx -xdy=xydx$

$ydx -xydx=xdy$

$ydx(1-x)=xdy$

$\frac{1-x}{x}dx=\frac{1}{y}dy$

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

Integrating both side,

$\int\ (\frac{1}{x}-1)} \,dx =\int\ (\frac{1}{y}) \,dy$

$log x-x=logy+c$

$logx-logy=x+c$

$log\frac{x}{y}=x+c$

$\frac{x}{y}=e^{x+c}$

The required solution of the differential equation is

$\frac{x}{y}=e^{x+c}$