Q. What is the solution to the differential equation y'' + 4y = 0?
A.y = C1 cos(2x) + C2 sin(2x)
B.y = C1 e^(2x) + C2 e^(-2x)
C.y = C1 e^(x) + C2 e^(-x)
D.y = C1 sin(2x) + C2 cos(2x)
Solution
This is a second-order linear homogeneous differential equation. The characteristic equation has roots ±2i, leading to the solution y = C1 cos(2x) + C2 sin(2x).
