Solve the differential equation.
$36 y ^ { tt } + y = 0$
A) $y ( x ) = c _ { 1 } \cos ( - 6 x ) + c _ { 2 } \sin ( - 6 x )$
B)$y ( x ) = c _ { 1 } \cos \left( - \frac { x } { 36 } \right) + c _ { 2 } \sin \left( - \frac { x } { 6 } \right)$
C)$y ( x ) = c _ { 1 } \cos \left( \frac { x } { 6 } \right) + c _ { 2 } \sin \left( \frac { x } { 6 } \right)$
D) $y ( x ) = c _ { 1 } \cos ( 6 x ) + c _ { 2 } \sin ( 6 x )$
E) $y ( x ) = c _ { 1 } \cos ( 36 x ) - c _ { 2 } \sin ( 36 x )$

Question

Quizplus · Accepted Answer

First, we can find the characteristic equation by assuming that $y=e^{rt}$:
$$36r^2+1=0 \rightarrow r=\pm\frac{i}{6}$$
Thus, the solution will be of the form:
$$y(x)=c_1\cos\left(\frac{x}{6}\right)+c_2\sin\left(\frac{x}{6}\right)$$
which matches choice C.

Solve the Differential Equation 36ytt+y=036 y ^ { tt } + y = 036ytt+y=0

Solve the Differential Equation $36 y ^ { tt } + y = 0$