Solve the differential equation. Select the correct answer.
$$y ^ { tt } - 8 y ^ { t } + 25 y = 0$$
A) $y = c e ^ { 4 x } \cos ( 3 x )$
B) $y = c _ { 1 } \cos ( 3 x ) + c _ { 2 } x \sin ( 3 x )$
C) $y = e ^ { 4 x } \left( c _ { 1 } \cos ( 3 x ) + c _ { 2 } \sin ( 3 x ) \right)$
D) $y = e ^ { 4 x } \left( c _ { 1 } \cos ( 3 x ) + c _ { 2 } x \sin ( 3 x ) \right)$
E) $y = e ^ { 4 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x ) \right)$

Question

Quizplus · Accepted Answer

The characteristic equation is $r^2 - 8r + 25 = 0$, which has complex roots $r = 4 \pm 3i$. The general solution is $y = e^{4x}(c_1 \cos(3x) + c_2 \sin(3x))$.

Solve the Differential Equation ytt−8yt+25y=0y ^ { tt } - 8 y ^ { t } + 25 y = 0ytt−8yt+25y=0

Solve the Differential Equation $y ^ { tt } - 8 y ^ { t } + 25 y = 0$