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)
$y = C _ { 1 } x + C _ { 2 } x \ln x + \frac { 23 } { 6 } x ( \ln x ) ^ { 3 }$

Question

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The Answer of 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)
$y = C _ { 1 } x + C _ { 2 } x \ln x + \frac { 23 } { 6 } x ( \ln x ) ^ { 3 }$

Solve the Differential Equation x2ytt−xyt+y=23xln⁡x given that y1=9x and x ^ { 2 } y ^ { tt } - x y ^ { t } + y = 23 x \ln x \text { given that } y _ { 1 } = 9 x \text { and }x2ytt−xyt+y=23xlnx given that y1​=9x and

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