AP 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
- A \(c x^2\)
- B \(c x\)
- C \(c x^3\)
- D \(c x^4\)
Answer & Solution
Correct Answer
(B) \(c x\)
Step-by-step Solution
Detailed explanation
Given that 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), \(v+x \frac{d v}{d x}=\frac{v x+x \tan \left(\frac{v x}{x}\right)}{x}\) \(\Rightarrow \quad x \frac{d v}{d x}=v+\tan v-v\)…
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