Since *y*''=3*y*, we obtain

and thus

Differentiating *y*''=3*y* yields

in particular

so

Since
*y*^{(4)}=3 *y*'', we get
*a*_{4}=9/4!=3/8.

One more time:
*y*^{(5)} = 3*y'''*, so
*a*_{5} = 3(- 3)/5! = - 3/40.

The Taylor approximation has the form

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