If y = y(x) is the solution of the differential equation (1 + e^ 2x )dy/dx + 2(1 + y^ 2 )e^ x = 0 and y(0) = 0, then 6(y'(0) + (y(log_e 3 ))^ 2 ) is equal to

JEE Main 2022 Mathematics question

If y = y(x) is the solution of the differential equation and y(0) = 0, then + ) is equal to

Answer: (3)

Separating variables, dy/(1 + ), so . With y(0) = 0: . So . Then \csc ^{2}\tan ^{-1}$ ·

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Question ID VK-035234