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Differential Equations: JEE Mains 2022 June 29 Shift 2

Medium· Variable separable· +4 / −1

If

y=y(x)

is the solution of the differential equation

\left(1+e^{2x}\right)\dfrac{dy}{dx}+2\left(1+y^2\right)e^x=0

and

y(0)=0

, then

6\left[y'(0)+\left(y\left(\log_e\sqrt3\right)\right)^2\right]

is equal to :

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