BUILT-IN MATHEMATICA SYMBOL

DifferentialRoot

DifferentialRoot[lde]
represents a function that solves the linear differential equation specified by

.

MORE INFORMATION

DifferentialRoot works like Function.

DifferentialRoot[lde][s] finds the value of the solution to the differential equation at the specific point s.

DifferentialRoot[lde] essentially gives a representation of the solution for y in DSolve.

DifferentialRoot is generated by functions such as Integrate, DSolve, and GeneratingFunction.

Functions such as Integrate, D, and Series can be used on DifferentialRoot objects.

DifferentialRoot[lde][{s₁, s₂, ...}], etc. threads automatically over lists.

DifferentialRootReduce can be used to reduce combinations of DifferentialRoot objects and other functions to a single DifferentialRoot object.

FunctionExpand will attempt to expand DifferentialRoot objects in terms of ordinary special and elementary functions.

DifferentialRoot represents a solution restricted to avoid cuts in the complex plane defined by , where can contain equations and inequalities.

EXAMPLES

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Basic Examples (2)

Define f to be the sin function:

Plot its result:

Solve a differential equation:

Numerical values:

Define f to be the sin function:

In[1]:=

Out[1]=

Plot its result:

In[2]:=

Out[2]=

Solve a differential equation:

In[1]:=

Out[1]=

Numerical values:

In[2]:=

Out[2]=

Scope (5)

Simple exact values are generated automatically:

DifferentialRoot threads element-wise over lists:

DifferentialRoot works on rational coefficients:

Inhomogeneous linear recurrences:

Solutions of a differential equation:

Generalizations & Extensions (1)

Equations with holonomic constant terms are automatically lifted to polynomial coefficients:

Applications (1)

Find the DifferentialRoot object of a special function:

Compute integrals:

Properties & Relations (5)

Extract the differential equation from a DifferentialRoot object:

Extract branch cuts if any:

Use DifferentialRootReduce to generate DifferentialRoot objects:

Integrate a DifferentialRoot object:

Find coefficients of the expansion of a DifferentialRoot object: