Introduction Linear Optimization Numerical Nonlinear Local Optimization

The general solution to a differential equation contains undetermined coefficients that are labeled C[1], C[2], and so on. This example has one undetermined parameter, C[1]. ...

There are four major areas in the study of ordinary differential equations that are of interest in pure and applied science. Of these four areas, the study of exact solutions ...

A partial differential equation (PDE) is a relationship between an unknown function u(x_1,x_2,…,x_n) and its derivatives with respect to the variables x_1,x_2,…,x_n. Here is ...

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve. The first three equations in this system of four nonlinear ODEs can be ...

Mathematica allows you to export graphics and sounds in a wide variety of formats. If you use the notebook front end for Mathematica, then you can typically just copy and ...

A Frobenius equation is an equation of the form where a_1, …, a_n are positive integers, m is an integer, and the coordinates x_1, …, x_n of solutions are required to be ...

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