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

question 49

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

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