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