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

Question

Quizplus · Accepted Answer

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

Solve the Differential Equation Using the Method of Undetermined Coefficients y′′−3y′=sin⁡9xy ^ { \prime \prime } - 3 y ^ { \prime } = \sin 9 xy′′−3y′=sin9x

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