Question

Evaluate : $(x+y)(dx-dy)=dx+dy$

Answer 1

given $(x+y)(dx-dy)=dx+dy$

$xdx-xdy+ydx-ydy=dx+dy$

Integrationg both sides

$\Rightarrow \int x.dx-\int x.dy+\int ydx-\int ydy=\int dx+\int dy$

$\Rightarrow \frac{x^2}{2}-x\int dy+y\int dx-\frac{y^2}{2}=\int dx+\int dy$

$\Rightarrow \frac{x^2}{2}-xy+yx-\frac{y^2}{2}=x+y+c$

$\Rightarrow \frac{x^2-y^2}{2}=x+y+c$

$\Rightarrow x^2-y^2=2x+2y+c$

$\Rightarrow x^2-y^2-2x-2y=c$