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

question 20

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

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