COMEDK · Maths · 32. Differential Equations
If \(\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x}\), then \(\sin \left(\frac{y}{x}\right)=\)
- A \(c x^{2}\)
- B \(c x\)
- C \(c x^{3}\)
- D \(\log x\)
Answer & Solution
Correct Answer
(B) \(c x\)
Step-by-step Solution
Detailed explanation
We have, \(\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x} \quad \text{...(i)}\) Given, differential equation is in homogeneous form. \(\therefore\) put \(y=v x\) in Eq. (i), we get \(v+x \frac{d v}{d x}=v+\tan v \Rightarrow \frac{1}{\tan v} d v=\frac{d x}{x}\) Taking integration…
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