Solve the differential equation. Select the correct answer.
$$y ^ { tt } - 4 y ^ { t } + 13 y = 0$$
A) $y ( x ) = c e ^ { 2 x } \cos ( 3 x )$
B) $y ( x ) = e ^ { 2 x } \left( c _ { 1 } \cos ( 3 x ) + c _ { 2 } x \sin ( 3 x ) \right)$
C) $y ( x ) = e ^ { 2 x } \left( c _ { 1 } \cos ( 3 x ) + c _ { 2 } \sin ( 3 x ) \right)$
D) $y ( x ) = e ^ { 3 x } \left( c _ { 1 } \cos ( 2 x ) + c _ { 2 } \sin ( 2 x ) \right)$
E) $y ( x ) = e ^ { 2 x } \left( c _ { 1 } \cos ( 2 x ) + c _ { 2 } x \sin ( 2 x ) \right)$

Question

Quizplus · Accepted Answer

The characteristic equation of the differential equation is $r^2 - 4r + 13 = 0$, which has complex roots $r = 2 \pm 3i$. The general solution for such roots is $y(x) = e^{2x}(c_1 \cos(3x) + c_2 \sin(3x))$.

Solve the Differential Equation ytt−4yt+13y=0y ^ { tt } - 4 y ^ { t } + 13 y = 0ytt−4yt+13y=0

Solve the Differential Equation $y ^ { tt } - 4 y ^ { t } + 13 y = 0$