JEE MAIN - Mathematics Hindi (2024 - 8th April Morning Shift - No. 9)

माना अवकल समीकरण $$\left(1+y^2\right) e^{\tan x} d x+\cos ^2 x\left(1+e^{2 \tan x}\right) d y=0, y(0)=1$$ का हल $$y=y(x)$$ हे। तो $$y\left(\frac{\pi}{4}\right)$$ बराबर हे
$$\frac{1}{e^2}$$
$$\frac{2}{e^2}$$
$$\frac{2}{e}$$
$$\frac{1}{e}$$

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