Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

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

1) log y = tan x (dy / dx)

2) y log y = tan x (dy / dx)

3) y log y = sin x (dy / dx)

4) log y = cos x (dy / dx)

5) y log y = cos x (dy / dx)

Solution: (2) y log y = tan x (dy / dx)

\(\begin{array}{l}\begin{array}{l} y=e^{\operatorname{asin} x}\\ \text { Taking log both sides }\\ \begin{array}{l} \sin x=\frac{\log y}{a} \\ \therefore \frac{d y}{d x}=e^{a \sin x} \cdot \mathrm{a} \cos x \\ \quad=y \cos x \cdot \frac{\log y}{\sin x} \\ \Rightarrow y \log y=\tan x \frac{d y}{d x} \end{array} \end{array}\end{array} \)

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