Ordinary differential equations

Abstract

A large part of the natural phenomena occurring in physics, engineering and other applied sciences can be described by a mathematical model, a collection of relations involving a function and its derivatives. The example of uniformly accelerated motion is typical, the relation being

$$ \frac{{d^2 s}} {{dt^2 }} = g, $$

((11.1))

where s = s(t) is the motion in function of time t, and g is the acceleration. Another example is radioactive decay. The rate of disintegration of a radioactive substance in time is proportional to the quantity of matter:

$$ \frac{{dy}} {{dt}} = - ky, $$

((11.2))

in which y = y(t) is the mass of the element and k > 0 the decay constant. The above relations are instances of differential equations.