WBJEE · Maths · Differential Equations
If \(x \sin \left(\frac{y}{x}\right) d y=\left[y \sin \left(\frac{y}{x}\right)-x\right] d x, x>0\) and \(y(1)=\frac{\pi}{2}\) then the value of \(\cos \left(\frac{y}{x}\right)\) is
- A 1
- B \(\log x\)
- C \(\mathrm{e}\)
- D 0
Answer & Solution
Correct Answer
(B) \(\log x\)
Step-by-step Solution
Detailed explanation
Hint: \(\operatorname{sinv}\left(v+x \cdot \frac{d v}{d x}\right)=v \sin v-1\) \(\Rightarrow \mathrm{x} \sin \mathrm{v} \cdot \frac{\mathrm{dv}}{\mathrm{dx}}=-1\) \(\Rightarrow \int \sin v \mathrm{~d} v=-\int \frac{\mathrm{dx}}{\mathrm{x}}\)…
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