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TS EAMCET · Maths · Differential Equations

If \(\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x}\), then \(\sin \frac{y}{x}\) is equal to

  1. A \(c x^2\)
  2. B \(c x\)
  3. C \(c x^3\)
  4. D \(c x^4\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(c x\)

Step-by-step Solution

Detailed explanation

Given that \(\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x}\) ...(i) This is a homogeneous differential equation. Put \(y=v x\) and \(\frac{d y}{d x}=v+x \frac{d v}{d x}\) From Eq. (i), \(v+x \frac{d v}{d x}=\frac{v x+x \tan \left(\frac{v x}{x}\right)}{x}\)…