Question

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)

• A. $4xy=x^{2}-3y+c$
• B. $xy=x^{2}-y^{2}+c$
• C. $xy=x^{2}+3y^{2}+c$
• D. $xy=x^{2}+c$

Answer 1

Answer: (C)

Given equation is $xdy-6ydy=2xdx-ydx$
$\Rightarrow xdy+ydx=2xdx+6ydy$
or $d\left(x y\right)=2xdx+6ydy$
On integrating, we get,
$xy=x^{2}+3y^{2}+c$