DifferentialRoot[lde] represents a function that solves the linear differential equation specified by lde[y, x].

When you write down a set of simultaneous equations in Mathematica, you are specifying a collection of constraints between variables. When you use Solve, you are finding ...

If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...

Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

DiscreteLyapunovSolve[a, c] finds the numeric solution x of the discrete matrix equation a.x.a\[ConjugateTranspose] - x == c.DiscreteLyapunovSolve[a, b, c] solves a.x.b - x ...

When you give a list of equations to Solve, it assumes that you want all the equations to be satisfied simultaneously. It is also possible to give Solve more complicated ...

LyapunovSolve[a, c] finds a solution x of the matrix Lyapunov equation a.x + x.a\[ConjugateTranspose] == c.LyapunovSolve[a, b, c] solves a.x + x.b == c.LyapunovSolve[{a, d}, ...

There are some close connections between finding a "local minimum" and solving a set of nonlinear equations. Given a set of n equations in n unknowns, seeking a solution r(x) ...

One of the important features of Mathematica is its ability to give you exact, symbolic, results for computations. There are, however, computations where it is just ...

FindRoot[f, {x, x_0}] searches for a numerical root of f, starting from the point x = x_0.FindRoot[lhs == rhs, {x, x_0}] searches for a numerical solution to the equation lhs ...