Q. The family of curves $y = e^{a\sin x}$, where $a$ is an arbitrary constant, is represented by the differential equation
A) $\log y = \tan x\frac{dy}{dx}$
B) $y\log y = \tan x\frac{dy}{dx}$
C) $y\log y = \sin x\frac{dy}{dx}$
D) $\log y = \cos x\frac{dy}{dx}$
Explanation
(b)
Curve is $y = e^{a\sin x} \Rightarrow \sin x = \frac{\log y}{a}$
$\therefore$ $\frac{dy}{dx} = e^{a\sin x}\ a\cos x$
$\Rightarrow$ $\frac{dy}{dx} = y\cos x.\frac{\log y}{\sin x}$
$\Rightarrow$ $y\log y = \tan x\ \frac{dy}{dx}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.