GATE_AE_2027_MOCK_04_Q38
GATE 2027 Aerospace Engineering All-India Master Mock 04 (Aerospace Structures, Thin-Walled Beams & Aeroelasticity)
NAT · 2 Marks
Engineering Mathematics • Differential Equations • Second Order Linear ODEs & Boundary Value Problems
Consider the boundary value problem d^2 y / dx^2 + 9 y = 0 with y(0) = 0 and y'(0) = 6. What is the value of y(\pi / 6)?
Answer Key:
2
Step-by-Step Verified Solution
### Solution: General solution: y(x) = A cos(3x) + B sin(3x). y(0) = A = 0. y'(x) = 3B cos(3x) ==> y'(0) = 3B = 6 ==> B = 2. y(x) = 2 sin(3x). At x = \pi / 6: 3x = \pi / 2 ==> y(\pi / 6) = 2 sin(\pi / 2) = 2 * 1 = 2. Correct: 2.