Use Power Series to Solve the Differential Equation $y ^ { \prime \prime } = 25 y$

Multiple Choice

Use power series to solve the differential equation. $y ^ { \prime \prime } = 25 y$

A) $y ( x ) = c _ { 1 } \cosh 5 x + c _ { 2 } \sinh 5 x$
B) $y ( x ) = c _ { 1 } 5 \cosh x + c _ { 2 } 5 \sinh x + e ^ { x }$
C) $y ( x ) = 5 \cosh x + 5 \sinh x$
D) $y ( x ) = c _ { 1 } \cosh 5 x + c _ { 2 } \sinh 5 x + e ^ { x }$
E) $y ( x ) = c _ { 1 } \cosh 5 x + c _ { 2 } \sinh 5 x + x ^ { 2 }$