If a first-order ordinary differential
equation in y(*t*) is prescribed to have a fixed value
y(*t*_{0}) = *y*_{0}, then problem of finding
a function y(*t*) which satisfies both of these conditions
is termed an *initial-value problem* (IVP).

To begin, we will look specifically at solving linear first-order ODEs of the form:

where a(*t*) and b(*t*) are known functions.

This topic looks at a three techniques for solving first-order linear IVPs, each of which is an improvement on the previous. Then we will look at other improvements and a technique for converting a higher-order IVP into a system of first-order IVPs is given.

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.