Mixed approximation vs. full approximation for a power series expansion

Hi PF, I'm trying to find an approximate solution of a differential equation that can't be solved in exact form. The differential equation is of the form: $$ f'(t)=g(f(t),t) $$ I want to find the approximate solution in terms of a power series: $$ f(t) \approx f(0) + f'(0) \cdot t +... Read more