A Clairaut equation is a first-order equation of the form A remarkable feature of this nonlinear equation is that its general solution has a very simple form. This is an ...

A linear second-order ordinary differential equation is said to be exact if An exact linear second-order ODE is solved by reduction to a linear first-order ODE.

Solving linear first-order ODEs is straightforward and only requires the use of a suitable integrating factor. In sharp contrast, there are a large number of methods ...

Systems of ODEs are important in various fields of science, such as the study of electricity and population biology. Like single ODEs, systems of ODEs can classified as ...

The following is a linear first-order ODE because both y[x] and y^ ′[x] occur in it with power 1 and y^′[x] is the highest derivative. Note that the solution contains the ...

An Euler equation has the general form Euler equations can be solved by transforming them to equations with constant coefficients. This is an example of an Euler equation.

The Basic Constructs Classes of Functionality Options Syntax

To run Mathematica using a network license, both the client machine and the license server must be on the network, and MathLM must be running. If you do not have a MathLM ...

Introduction Random Generation Functions Seeding and Localization

Introduction Methods for Local Minimization Methods for Solving Nonlinear Equations