The simplest type of linear second-order ODE is one with constant coefficients. This linear second-order ODE has constant coefficients. Notice that the general solution is a ...

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 ...

With its convenient symbolic representation of algebraic numbers, Mathematica's state-of-the-art algebraic number theory capabilities provide a concrete implementation of one ...

A linear ODE with constant coefficients can be easily solved once the roots of the auxiliary equation (or characteristic equation) are known. Some examples of this type ...

The following is a linear first-order ODE because both y[x] and y^ ′[x] occur in it with power 1 and y^′[x] is the highest derivative. Note that the solution contains the ...

A linear ordinary differential equation of order n is said to be exact if The condition of exactness can be used to reduce the problem to that of solving an equation of order ...

MaxExtraConditions is an option to Solve and related functions that specifies how many extra equational conditions on continuous parameters to allow in solutions that are ...

RootMeanSquare[list] gives the root mean square of values in list.

An Euler equation is an ODE of the form The following is an example of an Euler equation. The Legendre linear equation is a generalization of the Euler equation. It has the ...

The ODEs that arise in practical applications often have non-rational coefficients. In such cases, DSolve attempts to convert the equation into one with rational coefficients ...