Compute a Series Solution (AsymptoticDSolveValue)
A linear ordinary differential equation can be approximated by a Taylor series expansion 
near an ordinary point 
for the equation. This example shows how to obtain such an approximation using AsymptoticDSolveValue.
Compute a Taylor polynomial approximation for the defining ODE of Cos.
Improve the range of the approximation by specifying a higher order.
Study the variation of range with the order of the approximation.
Compute a Taylor approximation for a system of linear ODEs at the ordinary point 
.
Taylor approximations can often be computed for nonlinear ODEs with analytic coefficients, as illustrated by the following example.
Plot the successive approximations given by the solution.
