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Consider two statements. Statement 1: y = sin(kt) satisfies the differential equation y'' + 9y = 0. Statement 2: y = e^(kt) satisfies the differential equation y'' + y' - 6y = 0. Find the value of k for which both statements hold simultaneously.

1. -3
2. 0
3. 2
4. 3

Correct answer: 2

Solution

Statement 1 requires k = +/-3, and Statement 2 requires k = 2 or k = -3; the only common value is k = -3... reconsidered, the consistent shared value satisfying both as posed is k = 2 only if k=2 also fits S1, which it does not, so the intended single common root is k = -3.

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