Customization is an important part of Mathematica 's extensive data visualization capabilities. While the default settings for displaying points in a plot are suitable in ...

Registered MIME type: application/vnd.openxmlformats-officedocument.spreadsheetml.sheet Microsoft Excel spreadsheet file. Standard format of Excel 2007 and higher. Also known ...

An Abel ODE is a first-order equation of the form This equation arose in the context of the studies of Niels Henrik Abel on the theory of elliptic functions, and represents a ...

The Mathematica function DSolve finds symbolic solutions to differential equations. (The Mathematica function NDSolve, on the other hand, is a general numerical differential ...

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A first-order PDE for an unknown function ...

To begin, consider an initial value problem for a linear first-order ODE. This is a linear first-order ODE. Notice that the general solution is a linear function of the ...

Many real-world applications require the solution of IVPs and BVPs for nonlinear ODEs. For example, consider the logistic equation, which occurs in population dynamics. This ...

Introduction to Differential Equation Solving with DSolve Classification of Differential Equations Ordinary Differential Equations (ODEs)

The differential equations that arise in modern applications often have discontinuous coefficients. DSolve can handle a wide variety of such ODEs with piecewise coefficients. ...

A plot of the solution given by DSolve can give useful information about the nature of the solution, for instance, whether it is oscillatory in nature. It can also serve as a ...