Mathematical Analysis I pp 387-421 | Cite as

# Ordinary differential equations

Chapter

## Abstract

A large part of the natural phenomena occurring in physics, engineering and other applied sciences can be described by a where in which

*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)

*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)

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

Ordinary Differential Equation General Solution Homogeneous Equation Singular Integral Lipschitz Constant
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Italia, Milan 2008