Q. If $c$ is an arbitrary constant, then the general solution of the differential equation $y\ dx - x\ dy = xy\ dx$ is given by
A) $y = cxe^{- x}$
B) $y = cye^{- x}$
C) $y + e^{x} = cx$
D) $ye^{x} = cx$
Explanation
(d)
Given, $y(1 - x)dx = xdy$
$\Rightarrow$ $\left( \frac{1}{x} - 1 \right)dx = \frac{1}{y}dy$
$\Rightarrow$ $\log x - x = \log y - \log c$ [integrating]
$\Rightarrow$ $x = \log\frac{xc}{y}$
$\Rightarrow$ $ye^{x} = xc$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.