Use Power Series to Solve the Differential Equation $y ^ { \prime \prime } - x y ^ { \prime } - y = 0 , y ( 0 ) = 7 , y ^ { \prime } ( 0 ) = 0$

question 26

Multiple Choice

Use power series to solve the differential equation. $y ^ { \prime \prime } - x y ^ { \prime } - y = 0 , y ( 0 ) = 7 , y ^ { \prime } ( 0 ) = 0$

• A) \(y ( x ) = 7 e ^ { x }\)
• B) \(y ( x ) = 7 e ^ { - \frac { x ^ { 2 } } { 2 } }\)
• C) \(y ( x ) = e ^ { 7 x }\)
• D) \(y ( x ) = c e ^ { \frac { x ^ { 2 } } { 2 } }\)
• E) \(y ( x ) = 7 e ^ { \frac { x ^ { 2 } } { 2 } }\)

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