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AP EAMCET · Maths · Differential Equations

The general solution of the differential equation \(\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x\) is

  1. A \(\cos \frac{x}{y}=\log _e x+c\)
  2. B \(\cos \frac{y}{x}=\log _e x+c\)
  3. C \(\cos \frac{x}{y}=\log _e y+c\)
  4. D \(\cos \frac{y}{x}=\log _e y+c\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\cos \frac{y}{x}=\log _e x+c\)

Step-by-step Solution

Detailed explanation

\(\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x\) \(\frac{d y}{d x}=\frac{y \sin \frac{y}{x}-x}{x \sin \frac{y}{x}} \Rightarrow \frac{d y}{d x}=\frac{y}{x}-\operatorname{cosec} \frac{y}{x}\) Let…