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