Let $\mathrm{x}=\mathrm{x}(\mathrm{y})$ be the solution of the differential equation $ y=\left(x-y \frac{d x}{d y}\right) \sin \left(\frac{x}{y}\right), y0 \text { and } x(1)=\frac{\pi}{2}.$ Then $\cos (x(2))$ is equal to : [JEE Main 2025, 23 Jan (Shift 2)]

Question

Let $\mathrm{x}=\mathrm{x}(\mathrm{y})$ be the solution of the differential equation $ y=\left(x-y \frac{d x}{d y}\right) \sin \left(\frac{x}{y}\right), y>0 \text { and } x(1)=\frac{\pi}{2}.$ Then $\cos (x(2))$ is equal to : [JEE Main 2025, 23 Jan (Shift 2)]

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Let \(\mathrm{x}=\mathrm{x}(\mathrm{y})\) be the solution of the differential equation \( y=\left(x-y \frac{d x}{d y}\ri…

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