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Let \( y=y(x) \) be the solution of the differential equation, \( \frac{d \mathrm{y}}{\mathrm{dx}}+\mathrm{y} \tan \mathrm{x}=2 \mathrm{x}+\mathrm{x}^{2} \tan \mathrm{x}, \quad \) [JEE Main - 2019(Apri \( ] \) ]
P
W)
\( x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \), such that \( y(0)=1 \). then :
(a) \( \mathrm{y}^{\prime}\left(\frac{\pi}{4}\right)+\mathrm{y}^{\prime}\left(\frac{-\pi}{4}\right)=-\sqrt{2} \)
(b) \( \mathrm{y}^{\prime}\left(\frac{\pi}{4}\right)-\mathrm{y}^{\prime}\left(\frac{-\pi}{4}\right)=\pi-\sqrt{2} \)
(c) \( y\left(\frac{\pi}{4}\right)-y\left(-\frac{\pi}{4}\right)=\sqrt{2} \)
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