McLaurin expansion

by Marianna Kalwat   Last Updated January 19, 2018 01:20 AM

I've got an example and I wanted to know how it is expanded. Thanks for help.

$$h''(x)+2h'(x)+h(x)=0$$

$$h(x)=5xe^{-x}+2e^{-x}$$

Is converted to

$$h(x)={\sum _{n=0}^{\infty } \frac{5n{(-1)}^{n+1}x^n}{n!}}+{\sum _{n=0}^{\infty } \frac{2(-x)^n}{n!}}$$

I wanted to do this with

$$p(x)=7xe^{x}+5e^{-x}$$



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