Show That $f ( x ) = \sum _ { n = 0 } ^ { \infty } \frac { ( 8 x ) ^ { n } } { n ! }$

question 49

Essay

Show that $f ( x ) = \sum _ { n = 0 } ^ { \infty } \frac { ( 8 x ) ^ { n } } { n ! }$ is a solution to the differential equation $\frac { d y } { d x } = 8 y$ .

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