Question

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

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

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
$x^{2}+y^{2}-x y+x+y=c$