Solve the differential equation using the method of undetermined coefficients.
$$y ^ { tt } + 5 y ^ { t } + 6 y = 2 x ^ { 2 }$$
A)
$y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 9 } { 108 } c _ { 3 }$
B) $y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 1 } { 6 } x ^ { 2 }$
C) $y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x }$
D) $y ( x ) = \frac { 1 } { 6 } x ^ { 2 } - \frac { 5 } { 18 } x + \frac { 19 } { 108 }$
E) $y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 1 } { 3 } x ^ { 2 } - \frac { 5 } { 9 } x + \frac { 19 } { 54 }$

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The Answer of Solve the differential equation using the method of undetermined coefficients.
$$y ^ { tt } + 5 y ^ { t } + 6 y = 2 x ^ { 2 }$$
A)
$y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 9 } { 108 } c _ { 3 }$
B) $y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 1 } { 6 } x ^ { 2 }$
C) $y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x }$
D) $y ( x ) = \frac { 1 } { 6 } x ^ { 2 } - \frac { 5 } { 18 } x + \frac { 19 } { 108 }$
E) $y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 1 } { 3 } x ^ { 2 } - \frac { 5 } { 9 } x + \frac { 19 } { 54 }$

Solve the Differential Equation Using the Method of Undetermined Coefficients ytt+5yt+6y=2x2y ^ { tt } + 5 y ^ { t } + 6 y = 2 x ^ { 2 }ytt+5yt+6y=2x2

Solve the Differential Equation Using the Method of Undetermined Coefficients $y ^ { tt } + 5 y ^ { t } + 6 y = 2 x ^ { 2 }$