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

Question

The general solution of the differential equation (2x - y + 1)dx + (2 y - x + 1)dy = 0 is (A) x2 +y2 + xy - x + y = C (B) x2 + y2 - xy + x + y = C (C) x2 - y2 + 2xy - x + y = C (D) x2 - y2 - 2 xy + x - y = C

Tardigrade Admin · Accepted Answer

Given differential equation is (2 x-y+1) d x+(2 y-x+1) d y=0 ⇒ 2 x d x+2 y d y-(y d x+x d y)+d x+d y=0 ⇒ (2 x d x+2 y d y)-d(x y)+d x+d y=0 On integrating both sides, we get x2+y2-x y+x+y=c

Q. The general solution of the differential equation $(2 x - y + 1) d x + (2 y - x + 1) d y = 0$ is

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

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

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

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

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

Q. The general solution of the differential equation (2x−y+1)dx+(2y−x+1)dy=0 is

x2+y2+xy−x+y=C

x2+y2−xy+x+y=C

x2−y2+2xy−x+y=C

x2−y2−2xy+x−y=C