Use a Power Series to Solve the Differential Equation $$y ^ { tt } - 25 y = 0$$

question 4

Multiple Choice

Use a power series to solve the differential equation $$y ^ { tt } - 25 y = 0$$

• A) \(y = C _ { 0 } e ^ { 5 x } + C _ { 1 } e ^ { - 5 x }\), where \(C _ { 0 }\) and \(C _ { 1 }\) are arbitrary constants
• B) \(y = C _ { 0 } x + C _ { 1 } e ^ { 5 x }\), where \(C _ { 0 }\) and \(C _ { 1 }\) are arbitrary constants
• C) \(y = C _ { 0 } x + C _ { 1 } e ^ { - 5 x }\), where \(C _ { 0 }\) and \(C _ { 1 }\) are arbitrary constants
• D) \(y = \left( C _ { 0 } + C _ { 1 } x \right) e ^ { - 5 x }\), where \(C _ { 0 }\) and \(C _ { 1 }\) are arbitrary constants
• E) \(y = \left( C _ { 0 } + C _ { 1 } x \right) e ^ { 5 x }\), where \(C _ { 0 }\) and \(C _ { 1 }\) are arbitrary constants

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