Question

The general solution of the differential equation $(2x - y + 1) dx + (2y - x + 1) dy = 0$ is :

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

Answer 1

Answer: (B)

Given differential equation is
$(2 x-y+1) d x+(2 y-x+1) d y=0$
$\Rightarrow 2 x\, d x+2 y\, d y-(y\, d x+ x\, d y)+d x+ d y=0$
$\Rightarrow (2 x\, d x+2 y\, d y)-d(x y)+d x +d y=0$
On integrating both sides, we get
$x^{2}+y^{2}-x y +x +y=c$