JEE Mains · Maths · STD 12 - 9. differential equations
If \(\sin \left(\frac{y}{x}\right)=\log _0|x|+\frac{\alpha}{2}\) is the solution of the differential equation \(x \cos \left(\frac{y}{x}\right) \frac{d y}{d x}=y \cos \left(\frac{y}{x}\right)+x\) and \(y(1)=\frac{\pi}{3}\), then \(\alpha^2\) is equal to
- A \(3\)
- B \(12\)
- C \(4\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
Differential equation :- \( x \cos \frac{y}{x} \frac{d y}{d x}=y \cos \frac{y}{x}+x \) \( \cos \frac{y}{x}\left[x \frac{d y}{d x}-y\right]=x\) Divide both sides by \(\mathrm{x}^2\) \(\cos \frac{y}{x}\left(\frac{x \frac{d y}{d x}-y}{x^2}\right)=\frac{1}{x}\) Let \(\frac{y}{x}=t\)…
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