Solve the Differential Equation $x ^ { 2 } y ^ { tt } - x y ^ { t } + y = 23 x \ln x \text { given that } y _ { 1 } = 9 x \text { and }$

Multiple Choice

Solve the differential equation $x ^ { 2 } y ^ { tt } - x y ^ { t } + y = 23 x \ln x \text { given that } y _ { 1 } = 9 x \text { and }$ $y _ { 2 } = 9 x \ln x$ are solutions of the corresponding homogeneous equation.

A)
$y = C _ { 1 } 9 x + C _ { 2 } 9 x \ln x - \frac { 23 } { 45 } x ( \ln x ) ^ { 4 }$
B)
$y = C _ { 1 } 9 x + C _ { 2 } 9 x \ln x - \frac { 23 } { 63 } x ( \ln x ) ^ { 4 }$
C)
$y = C _ { 1 } 9 x + C _ { 2 } 9 x \ln x + \frac { 23 } { 90 } x ( \ln x ) ^ { 2 }$
D)
$y = C _ { 1 } 9 x + C _ { 2 } 9 x \ln x + \frac { 23 } { 72 } x ( \ln x ) ^ { 2 }$
E)
$y = C _ { 1 } x + C _ { 2 } x \ln x + \frac { 23 } { 6 } x ( \ln x ) ^ { 3 }$