Use Power Series to Solve the Differential Equation $$y ^ { t } = 4 x y .$$

Multiple Choice

Use power series to solve the differential equation. $$y ^ { t } = 4 x y .$$

A) $y ( x ) = c e ^ { - \frac { 4 x ^ { 2 } } { 2 } }$
B) $y ( x ) = c e ^ { \frac { 4 x ^ { 2 } } { 2 } }$
C) $y ( x ) = e ^ { - \frac { x ^ { 2 } } { 2 } }$
D) $y ( x ) = c e ^ { 4 x }$
E) $y ( x ) = 4 e ^ { \frac { x ^ { 2 } } { 2 } }$