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Friday, 9 October

JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2026, Shift 2, Maths Q19

Question 19 of 75 in this shift, Maths question 19 of 25, Section A.

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)=\frac32. If y(1)=α(2+e−2)y(1)=\alpha(2+e^{-2}), then α\alpha is equal to:
  1. (1)138\frac{13}{8}
  2. (2)613\frac{6}{13}
  3. (3)1213\frac{12}{13}
  4. (4)1312\frac{13}{12}Official answer

Official answer

Option 4

NTA final key.

Chapter
Differential Equations
Topic
Linear Differential Equations
Idea tested
Integrating Factor Calculation

Same idea in other shifts

Asked 3× in all
  1. 3 Apr 2025, Shift 1 · Q20Let gg be a differentiable function such that ∫0xg(t) dt=x−∫0xt g(t) dt\int_0^x g(t)\,dt = x - \int_0^x t\,g(t)\,dt, x≥0x \ge 0 and let y=y(x)y = y(x) satisfy the…HardSingle correct
  2. 13 Apr 2023, Shift 2 · Q27If y=y(x)y=y(x) is the solution of the differential equation dydx+4x(x2−1)y=x+2(x2−1)52\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}}, x>1x>1 such…HardNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.