JEE MAIN - Mathematics Hindi (2024 - 6th April Morning Shift - No. 16)
माना $$y=y(x)$$ अवकल समीकरण $$\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}, y(1)=0$$ का हल है, तो $$y(0)$$ है -
$$\frac{1}{4}\left(e^{\pi / 2}-1\right)$$
$$\frac{1}{2}\left(1-e^{\pi / 2}\right)$$
$$\frac{1}{4}\left(1-e^{\pi / 2}\right)$$
$$\frac{1}{2}\left(e^{\pi / 2}-1\right)$$
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