GATE_AE_2027_MOCK_04_Q14
GATE 2027 Aerospace Engineering All-India Master Mock 04 (Aerospace Structures, Thin-Walled Beams & Aeroelasticity)
NAT · 1 Mark
Engineering Mathematics • Differential Equations • First Order Ordinary Differential Equations
Solve the separable differential equation dy/dx = 2x y with initial condition y(0) = 1. What is the value of y(1)? (Take e ≈ 2.718, round to two decimal places).
Answer Key:
2.72
Step-by-Step Verified Solution
### Solution: dy/y = 2x dx ==> ln y = x^2 + C. With y(0) = 1, C = 0 ==> y = exp(x^2). At x = 1, y = e^1 ≈ 2.718 ≈ 2.72. Correct: 2.72 (range 2.70 to 2.74).