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Chapter 14: Initial-Value Problems
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## Chapter 14: Initial-Value Problems

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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:

y^{(1)}(*t*) = a(*t*) y(*t*) + b(*t*)
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.

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