![]() ![]() ![]() However, for most di erential equations, one must be content with approximate solutions. An important special case is when f is a linear function of y. ![]() ![]() In mathematics courses, one learns how to determine exact solutions to this problem for certain special functions f. To start with, we shall study the following problem: given a function f(t y), nd a function y(t) which for a t b is an approximate solution to the initial value problem for the ordinary di erential equation or, with an established abbreviation, the ODE, dy = f(t y) y(a) = c: (13.1.1) dt Theoretical Background 13.1.1 Introduction Ordinary Di erential Equations 13.1 Initial Value Problems for ODEs. ![]()
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