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Find the general solution of the differential equation d²y/dx² + a² y = 0.
- y = (c1 cos ax + c2 sin ax) e^(ax)
- y = c1 cos ax + c2 sin ax
- y = c1 e^(ax) + c2 e^(-ax)
- none of these
Correct answer: y = c1 cos ax + c2 sin ax
Solution
The characteristic equation m² + a² = 0 gives m = +- ia, so the solution is y = c1 cos ax + c2 sin ax.
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