While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

NSolve gives you a general way to find numerical approximations to the solutions of polynomial equations. Finding numerical solutions to more general equations, however, can ...

The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to ...

Numerical solution of differential equations. This generates a numerical solution to the equation y^′(x)y(x) with 0<x<2. The result is given in terms of an ...

DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...

A plot of the solution given by DSolve can give useful information about the nature of the solution, for instance, whether it is oscillatory in nature. It can also serve as a ...

A delay differential equation is a differential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times: ...

Solve[expr, vars] attempts to solve the system expr of equations or inequalities for the variables vars. Solve[expr, vars, dom] solves over the domain dom. Common choices of ...

NSolve[expr, vars] attempts to find numerical approximations to the solutions of the system expr of equations or inequalities for the variables vars. NSolve[expr, vars, ...

MatrixPower[m, n] gives the n\[Null]\[Null]^th matrix power of the matrix m. MatrixPower[m, n, v] gives the n\[Null]^th matrix power of the matrix m applied to the vector v.