Multiple choice

The general solution of $\frac{d^2y}{dx^2} + y = o $ is

  1. y = P cos x + Q sin x

  2. y = P cos x

  3. y = P sin x

  4. y = P sin2x
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A Correct answer
Explanation

The differential equation y'' + y = 0 has the characteristic equation r^2 + 1 = 0, which gives roots r = +/- i. The general solution is y = c1 cos(x) + c2 sin(x).

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