"Defining Variables" discussed assignments such as x=y which set x equal to y. Here we discuss equations, which test equality. The equation x==y tests whether x is equal to ...

Mathematica's symbolic architecture allows it to represent any equation as a symbolic expression that can be manipulated using any of Mathematica's powerful collection of ...

Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically ...

You can use the Mathematica function DSolve to find symbolic solutions to ordinary and partial differential equations. Solving a differential equation consists essentially in ...

Automatically selecting between hundreds of powerful and in many cases original algorithms, Mathematica provides both numerical and symbolic solving of differential equations ...

QuadraticIrrationalQ[x] gives True if x is a quadratic irrational and False otherwise.

The main equations that Solve and related Mathematica functions deal with are polynomial equations. It is easy to solve a linear equation in  x. One can also solve quadratic ...

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

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 ...

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}, ...