The values of m for which $y = e ^ { m x }$ is a solution of $y ^ { \prime \prime } - 6 y ^ { \prime } - 7 y = 0$ are
A) 1 and 7
B) $- 1$ and 6
C) 1 and 6
D) 1 and $- 6$
E) $- 1$ and 7

Question

Quizplus · Accepted Answer

To find the values of m, substitute $y = e^{mx}$ into the differential equation. The characteristic equation is $m^2 - 6m - 7 = 0$. Solving this quadratic equation gives the roots $m = -1$ and $m = 7$.

The Values of M for Which y=emxy = e ^ { m x }y=emx

The Values of M for Which $y = e ^ { m x }$