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

DifferenceRoot[lde] represents a function that solves the linear difference equation specified by lde[a, n].

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

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 ...

InverseFunctions is an option for Solve and related functions that specifies whether inverse functions should be used.

The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...

DiscreteRiccatiSolve[{a, b}, {q, r}] gives the matrix x that is the stabilizing solution of the discrete algebraic Riccati equation ConjugateTranspose[a].x.a - x - ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

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

RiccatiSolve[{a, b}, {q, r}] gives the matrix x that is the stabilizing solution of the continuous algebraic Riccati equation ConjugateTranspose[a].x + x.a - ...