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AP EAMCET · Maths · Differential Equations

If \(\cos \frac{y}{x}=A \log x+C\) is the general solution of \(\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x\), then \(A=\)

  1. A 2
  2. B 1
  3. C -1
  4. D -2
Verified Solution

Answer & Solution

Correct Answer

(B) 1

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { }\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x \\ & \frac{d y}{d x}=\frac{y \sin y / x-x}{x \sin \frac{y}{x}} \Rightarrow \frac{d y}{d x}=\frac{y}{x}-\frac{1}{\sin \frac{y}{x}} \\ & \text { Let } \frac{y}{x}=v \text { or }…