Question

Solution of the different equation, $ydx-xdy+x{y}^{2}dx=0$ can be.

• A. $2x+x^{2}y=\lambda y$
• B. $2y+y^{2}x=\lambda y$
• C. $2y-y^{2}x=\lambda y$
• D. none of these

Answer 1

The correct option is A $2x+x^{2}y=\lambda y$

$\frac{ydx-xdy}{y^2}=d\left(\frac{x}{y}\right)$

Hence,

$\frac{ydx-xdy}{y^2}+xdx=0$

$d\left(\frac{x}{y}\right)+xdx=0$

Integrating both sides we get,

$\frac{x}{y}+\frac{x^2}{2}=C$

$2x+x^{2}y=\lambda y$