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

DSolve[eqn, y, x] solves a differential equation for the function y, with independent variable x. DSolve[{eqn_1, eqn_2, ...}, {y_1, y_2, ...}, x] solves a list of ...

You can give Solve a list of simultaneous equations to solve. Solve can find explicit solutions for a large class of simultaneous polynomial equations. Here is a simple ...

Derivatives in Mathematica work essentially the same as in standard mathematics. The usual mathematical notation, however, often hides many details. To understand how ...

C[i] is the default form for the i\[Null]\[Null]^th parameter or constant generated in representing the results of various symbolic computations.

Introduction ODE Integration Methods Partial Differential Equations

The Mathematica function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations (ODEs) as well as some ...

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...

[AP91] Ascher, U. and L. Petzold. "Projected Implicit Runge–Kutta Methods for Differential Algebraic Equations." SIAM J. Numer. Anal. 28 (1991): 1097–1120. [AP98] Ascher, U. ...