Question

The family of curves y=easin x, where a is an arbitrary constant, is represented by the differential equation

• A. ylog y=tanx $\frac{dy}{dx}$
• B. ylog x=cotx $\frac{dy}{dx}$
• C. log y=tanx $\frac{dy}{dx}$
• D. log y=cotx $\frac{dy}{dx}$

Answer 1

Answer: (A)

ylog y=tanx $\frac{dy}{dx}$

Answer 2

The correct answer is option (A): ylog y=tanx $\frac{dy}{dx}$

$y=e^{a\,sin\,x}$

$\Rightarrow log\,y=a\,sin\,x....(i)$

Differentiating w.r.t $x$, we get

$\frac{1}{y}.\frac{dy}{dx}=a\,cos\,x$

$\Rightarrow a=\frac{1}{y\,cos\,x}\frac{dy}{dx}$

Putting the value of a in (I), we get,

ylog y=tanx $\frac{dy}{dx}$