# Program 02d: Power series solution of a second order ODE;
# example 8, chapter 2
from sympy import Function, dsolve, pprint
from sympy.abc import t

x = Function('x')
dxdt2 = x(t).diff(t, 2)
dxdt = x(t).diff(t)
ode = dxdt2+2*t**2*dxdt+x(t)
sol = dsolve(ode, hint='2nd_power_series_ordinary', n=6)
print('Solution:\n')
pprint(sol)