Question

The solution of differential equation $y^{2}xdx+ydx-xdy=0$ is
(where $C$ is constant of integration)

• A. $\frac{y^2}{2}+\frac{x}{y}+C=0$
• B. $\frac{x^2}{2}+\frac{x}{y}+C=0$
• C. $\frac{x^2}{2}+\frac{y}{x}+C=0$
• D. $\frac{y^2}{2}+\frac{y}{x}+C=0$

Answer 1

The correct option is B $\frac{x^2}{2}+\frac{x}{y}+C=0$

We have
$y^{2}xdx+ydx-xdy=0$
$\Rightarrow xdx+\frac{ydx-xdy}{y^2}=0$
$\Rightarrow xdx+d\left(\frac{x}{y}\right)=0$
Integrating both sides, we get
$\frac{x^2}{2}+\frac{x}{y}+C=0$