Q. The solution of the differential equation $\frac{dx}{x} + \frac{dy}{y} = 0$ is
A) $xy = c$
B) $x + y = c$
C) $\log{x\log{y = c}}$
D) $x^{2} + y^{2} = c$
Explanation
(a)
Given equation is $\frac{dx}{x} + \frac{dy}{y} = 0$
On integrating, we get
$\int_{}^{}{\frac{dx}{x} + \int_{}^{}{\frac{dy}{y} = 0}}$
$\Rightarrow \log{x + \log{y = \log c}}$
$\Rightarrow \log{(xy) + \log{c \Rightarrow {xy =}c}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.