Solve the differential equation using the method of undetermined coefficients.
$$y ^ { tt } - 3 y ^ { t } = \sin 9 x$$
A)
$y ( x ) = c _ { 1 } + c _ { 2 } e ^ { 3 x } - \frac { 1 } { 90 } \sin ( 6 x )$
B)
$y ( x ) = c _ { 1 } e ^ { 3 x } + \frac { 1 } { 90 } \cos ( 6 x ) + \frac { 1 } { 270 } \sin ( 6 x )$
C)
$y ( x ) = c _ { 1 } + c _ { 2 } e ^ { 3 x } + \frac { 1 } { 270 } \cos ( 6 x ) - \frac { 1 } { 90 } \sin ( 6 x )$
D)
$y ( x ) = c _ { 1 } e ^ { 3 x } + \frac { 1 } { 270 } \cos ( 6 x ) - \frac { 1 } { 90 } \sin ( 6 x )$
E)
$y ( x ) = \frac { 1 } { 270 } \cos ( 6 x ) - \frac { 1 } { 90 } \sin ( 6 x )$

Question

Quizplus · Accepted Answer

The complementary solution is $c_1 + c_2 e^{3x}$. The particular solution for $\sin 9x$ is of the form $A \cos 9x + B \sin 9x$. Solving gives $A = \frac{1}{270}$ and $B = -\frac{1}{90}$.

Solve the Differential Equation Using the Method of Undetermined Coefficients ytt−3yt=sin⁡9xy ^ { tt } - 3 y ^ { t } = \sin 9 xytt−3yt=sin9x

Solve the Differential Equation Using the Method of Undetermined Coefficients $y ^ { tt } - 3 y ^ { t } = \sin 9 x$