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

Introduction to Differential Equation Solving with DSolve Classification of Differential Equations Ordinary Differential Equations (ODEs)

DifferentialRootReduce[expr, x] attempts to reduce expr to a single DifferentialRoot object as a function of x.DifferentialRootReduce[expr, {x, x_0}] takes the initial ...

RecurrenceTable[eqns, expr, {n, n_max}] generates a list of values of expr for successive n based on solving the recurrence equations eqns.RecurrenceTable[eqns, expr, nspec] ...

Mathematica treats equations as logical statements. If you type in an equation like x^2+3x==2, Mathematica interprets this as a logical statement which asserts that x^2+3x is ...

NDSolve returns solutions as InterpolatingFunction objects. Most of the time, simply using these as functions does what is needed, but occasionally it is useful to access the ...

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 ...

While DSolve usually returns the correct solution to a differential equation it is given, it is common practice to verify the solution returned by any differential equation ...

DependentVariables is an option which specifies the list of all objects that should be considered as dependent variables in equations that have been supplied.

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 ...