Question

Find the general solution of given differential equation.

$\frac{dy}{dx}=\frac{x-y}{x+y}$ or $(x+y)dy-(x-y)dx=0$

• A. $y^2+2xy-x^2=k$
• B. $-y^2+2xy+x^2=k$
• C. $y^2-2xy-x^2=k$
• D. $y^2+2xy+x^2=k$

Answer 1

The correct option is A $y^2+2xy-x^2=k$

$\frac{dy}{dx}=\frac{x-y}{x+y}\Rightarrow (x+y)dy-(x-y)dx=0$
$\Rightarrow (xdy+ydx)+ydy-xdx=0$
$\Rightarrow d\left(xy\right)+ydy-xdx=0$
Integrating we get, $xy+\frac{y^2}{2}-\frac{x^2}{2}=c$
$\Rightarrow y^2+2xy-x^2=k$