Question

The general solution of differential equation $(x-y)dy+(x+y)dx=dx+dy$ is
(where $C$ is constant of integration )

• A. $xy-\frac{y^2}{2}+\frac{x^2}{2}=x+y+C$
• B. $xy+\frac{y^2}{2}-\frac{x^2}{2}=x+y+C$
• C. $2xy-\frac{y^2}{3}+\frac{x^2}{3}=x+y+C$
• D. $xy-\frac{y^2}{3}+\frac{x^2}{3}=x+y+C$

Answer 1

The correct option is A $xy-\frac{y^2}{2}+\frac{x^2}{2}=x+y+C$

The given equation can be written as
$(xdy+ydx)-ydy+xdx=dx+dy$
$\Rightarrow d\left(xy\right)-ydy+xdx=dx+dy$
Integrating both sides, we get
$xy-\frac{y^2}{2}+\frac{x^2}{2}=x+y+C$