Electrical Engineering > GATE 2026 > Differential Equations
Consider the second-order differential equation
d2y/dx2 + dy/dx + y = 0
with initial conditions y(0) = 1, dy/dx|x=0 = 1
The solution is given by
A
y(x) = exp(−x/2)(cos(√3x/2) + √3sin(√3x/2))
B
y(x) = exp(−x/2)(cos(√3x/2) + (1/√3)sin(√3x/2))
C
y(x) = exp(−x/2)(cos(√3x/2) − (1/√3)sin(√3x/2))
D
y(x) = exp(−x/2)(cos(√3x/2) − √3sin(√3x/2))

Correct : b

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