Question

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. $\log y=\cos x\frac{dy}{dx}$

Answer 1

The correct option is B $y\log y=\tan x\frac{dy}{dx}$

Curve is $y=e^{a\sin x}\Rightarrow \sin x=\frac{\log y}{a}$

$\therefore \frac{dy}{dx}=e^{a\sin x}.a\cos x$

$\Rightarrow \frac{dy}{dx}=y\cos x.\frac{\log y}{\sin x}$

$\Rightarrow y\log y=\tan x\frac{dy}{dx}$