For what nonzero values of $k$ does the function $y = A \sin k t + B \cos k t$ satisfy the differential equation $y ^ { \prime \prime } + 100 y = 0$ for all values of $A$ and $B$ ?
A) $k = 10$
B) $k = - 100$
C) $k = - 10$
D) $k = 100$
E) $k = 1$

Question

Quizplus · Accepted Answer

The differential equation $y'' + 100y = 0$ requires that the characteristic equation $k^2 + 100 = 0$ be satisfied. Solving gives $k^2 = -100$, so $k = \pm 10$.

For What Nonzero Values Of kkk Does the Function y=Asin⁡kt+Bcos⁡kty = A \sin k t + B \cos k ty=Asinkt+Bcoskt

For What Nonzero Values Of $k$ Does the Function $y = A \sin k t + B \cos k t$