Differential Equations
Q. What is the solution to the equation y'' + 4y = 0?
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A.
y = C1 cos(2x) + C2 sin(2x)
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B.
y = C1 e^(2x) + C2 e^(-2x)
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C.
y = C1 e^(4x) + C2 e^(-4x)
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D.
y = C1 sin(4x) + C2 cos(4x)
Solution
The characteristic equation is r^2 + 4 = 0, giving complex roots. The general solution is y = C1 cos(2x) + C2 sin(2x).
Correct Answer: A — y = C1 cos(2x) + C2 sin(2x)
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