Which equation does the function $y = e ^ { - 6 t }$ satisfy?
A) $y ^ {tt } - 3 y ^ { t } + 42 y = 0$
B) $y ^ { tt } - y ^ { t } - 42 y = 0$
C) $y ^ { tt } - y ^ { t } + 42 y = 0$
D) $y ^ { tt } + y ^ { t } - 42 y = 0$
E) $y ^ {tt } + y ^ { t } + 42 y = 0$

Question

Quizplus · Accepted Answer

The function $y = e^{-6t}$ has a characteristic equation with roots $r = -6$. Substituting $r = -6$ into the characteristic equation of option B, $(r^2 - r - 42 = 0)$, satisfies the equation.

Which Equation Does the Function y=e−6ty = e ^ { - 6 t }y=e−6t

Which Equation Does the Function $y = e ^ { - 6 t }$