This problem concerns the differential equation ’= ( ) where (0) = . (a) From the differentiation formula                 derive a difference equation that can be used to numerically solve the...

This problem concerns the differential equation
’=
() where
(0) =
.

(a) From the differentiation formula

derive a difference equation that can be used to numerically solve the differential equation.

(b) One of the curves in Figure 7.16 gives the error as a function of the number of grid points for the method you derived in part (a). Which one is it? Make sure to justify your answer.