Let the solution curve y = y (x) of the differential equation (1 + e^2x) (dy/dx + y) = 1

Let the solution curve y = y (x) of the differential equation (1 + e^2x) (dy/dx + y) = 1 pass through the point (0 , π/2). Then \(\lim\limits_{x \to \infty}\) e^xy(x) is equal to :

(A) π/4

(B) 3π/4

(D) 3π/2

Let the solution curve y = y (x) of the differential equation (1 + e^2x) (dy/dx + y) = 1

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