Use Power Series to Solve the Differential Equation $$y ^ {tt } = 36 y$$

Multiple Choice

Use power series to solve the differential equation. $$y ^ {tt } = 36 y$$

A) $y ( x ) = c _ { 1 } \cosh 6 x + c _ { 2 } \sinh 6 x$
B) $y ( x ) = 6 \cosh x + 6 \sinh x$
C) $y ( x ) = c _ { 1 } 6 \cosh x + c _ { 2 } 6 \sinh x + e ^ { x }$
D) $y ( x ) = c _ { 1 } \cosh 6 x + c _ { 2 } \sinh 6 x + e ^ { x }$
E) $y ( x ) = c _ { 1 } \cosh 6 x + c _ { 2 } \sinh 6 x + x ^ { 2 }$