The solution of the differential equation (d y/d x)=(2 x - y/x - 6 y) is (where c is an arbitrary constant)

Question

The solution of the differential equation (d y/d x)=(2 x - y/x - 6 y) is (where c is an arbitrary constant) (A) 4xy=x2-3y+c (B) xy=x2-y2+c (C) xy=x2+3y2+c (D) xy=x2+c

Tardigrade Admin · Accepted Answer

Given equation is xdy-6ydy=2xdx-ydx ⇒ xdy+ydx=2xdx+6ydy or d(x y)=2xdx+6ydy On integrating, we get, xy=x2+3y2+c

Q. The solution of the differential equation $\frac{d y}{d x} = \frac{2 x - y}{x - 6 y}$ is (where $c$ is an arbitrary constant)

$4 x y = x^{2} - 3 y + c$

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

$x y = x^{2} + 3 y^{2} + c$

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

Given equation is $x d y - 6 y d y = 2 x d x - y d x$
$\Rightarrow x d y + y d x = 2 x d x + 6 y d y$
or $d (x y) = 2 x d x + 6 y d y$
On integrating, we get,
$x y = x^{2} + 3 y^{2} + c$

Q. The solution of the differential equation dxdy​=x−6y2x−y​ is (where c is an arbitrary constant)

4xy=x2−3y+c

xy=x2−y2+c

xy=x2+3y2+c

xy=x2+c