Question

Solve: $(2x+y+3)dx=(2y+x+1)dy$

Answer 1

Given,

$(2x+y+3)dx=(2y+x+1)dy$

$2xdx+3dx-xdy=2ydy+dy-ydx$

integating on both sides, we get,

$2\times \frac{x^2}{2}+3x-\frac{x^2}{2}=2\times \frac{y^2}{2}+y-\frac{y^2}{2}$

$\frac{x^2}{2}+3x=\frac{y^2}{2}+y$

$x^2+6x=y^2+2y$

$x^2-y^2+6x-2y=0$