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MathsJEE Main 4 Apr 2026, Shift 2·Q19·MCQ·Tough

Differential Equations · Linear differential equations

Let y=y(x)y = y(x) be the solution of the differential equation: dydx+(6x2+(3x2+2x3+4)e−2x(x3+2)(2+e−2x))y=2+e−2x,\frac{dy}{dx} + \left(\frac{6x^2 + \left(3x^2 + 2x^3 + 4\right)e^{-2x}}{\left(x^3 + 2\right)\left(2 + e^{-2x}\right)}\right)y = 2 + e^{-2x}, x∈(−1,2)x \in (-1, 2), satisfying y(0)=32y(0) = \dfrac32. If y(1)=α(2+e−2)y(1) = \alpha\left(2 + e^{-2}\right), then α\alpha is equal to:
  1. (1)138\dfrac{13}{8}
  2. (2)613\dfrac{6}{13}
  3. (3)1213\dfrac{12}{13}
  4. (4)1312\dfrac{13}{12}
We corrected a printing error in the original paper

Source printed “than α\alpha is equal to”.

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