WBJEE · Maths · Differential Equations
The family of curves \(y=e^{a \sin x}\), where ' \(a\) ' is arbitrary constant, is represented by the differential equation
- A \(y \log y=\tan x \frac{d y}{d x}\)
- B \(y \log x=\cot x \frac{d y}{d x}\)
- C \(\log y=\tan x \frac{d y}{d x}\)
- D \(\log y=\cot x \frac{d y}{d x}\)
Answer & Solution
Correct Answer
(A) \(y \log y=\tan x \frac{d y}{d x}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \Rightarrow \log y=a \sin x \\ & \Rightarrow \frac{d}{d x}\left(\frac{\log y}{\sin x}\right)=\frac{d}{d x}(a) \Rightarrow \frac{\sin x\left(\frac{d y}{d x}\right)}{y}-\log y \times \cos x=0 \\ & \Rightarrow y \log y=\tan x \times \frac{d y}{d x}\end{aligned}\)
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