This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

DifferentialRoot

DifferentialRoot[lde]
represents a function that solves the linear differential equation specified by .
  • DifferentialRoot[lde][s] finds the value of the solution to the differential equation at the specific point s.
  • DifferentialRoot represents a solution restricted to avoid cuts in the complex plane defined by , where can contain equations and inequalities.
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]:=
Click for copyable input
Out[1]=
Plot its result:
In[2]:=
Click for copyable input
Out[2]=
 
Solve a differential equation:
In[1]:=
Click for copyable input
Out[1]=
Numerical values:
In[2]:=
Click for copyable input
Out[2]=
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:
Equations with holonomic constant terms are automatically lifted to polynomial coefficients:
Find the DifferentialRoot object of a special function:
Compute integrals:
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:
New in 7