Find the Series Solution of the Differential Equation $y ^ { tt } - 7 x y ^ { t } = 0 \text { given the initial }$

question 11

Multiple Choice

Find the series solution of the differential equation $y ^ { tt } - 7 x y ^ { t } = 0 \text { given the initial }$ conditions $y ( 0 ) = 0$ and $y ^ { t } ( 0 ) = 4$

• A) \(y = 4 \left( 1 + \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n + 1 } x ^ { 2 n + 1 } } { 2 ^ { n } n ! ( 2 n + 1 ) } \right)\)
• B)\(y = 4 \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n } x ^ { 2 n + 1 } } { 2 ^ { n } n ! ( 2 n + 1 ) }\)
• C)\(y = 4 \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n + 1 } x ^ { 2 n + 1 } } { 2 ^ { n } ( 2 n + 1 ) ! }\)
• D)\(y = 4 + \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n } x ^ { 2 n + 1 } } { 2 ^ { n } ( 2 n + 1 ) ! }\)
• E)\(y = 4 + \sum _ { n = 0 } ^ { \infty } \frac { 7 ^ { n } x ^ { 2 n + 1 } } { 2 ^ { n } n ! ( 2 n + 1 ) }\)

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