Q. The solution of the differential equation $y\ dx + \left( x + x^{2}y \right)dy = 0$ is
A) $- \frac{1}{xy} = c$
B) $- \frac{1}{xy} + \log y = c$
C) $\frac{1}{xy} + \log y = c$
D) $\log y = cx$
Explanation
(b)
Given, $\frac{y\ dx + x\ dy}{x^{2}y^{2}} = - \frac{1}{y}\ dy$
$\Rightarrow$ $d\left( - \frac{1}{xy} \right) = - \frac{1}{y}\ dy$
$\Rightarrow$ $- \frac{1}{xy} = - \log y + c$ [integrating]
$\Rightarrow$ $- \frac{1}{xy} + \log y = c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.