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

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