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Mathematica > Mathematics and Algorithms > Calculus > Differential Operators >

Built-in Mathematica Symbol

DifferentialRootReduce

DifferentialRootReduce[expr, x]
attempts to reduce expr to a single DifferentialRoot object as a function of x.

DifferentialRootReduce[expr, {x, x₀}]
takes the initial conditions to be specified at x=x₀.

DifferentialRootReduce will attempt to represent any expression as a DifferentialRoot object.

DifferentialRootReduce[expr, x] always gives exactly 0 when the DifferentialRoot object for expr is equivalent to the zero function.

DifferentialRootReduce automatically threads over lists, as well as equations and inequalities.

DifferentialRootReduce[f] operates on a pure function or pure DifferentialRoot object.

Reduce the Bessel function to a DifferentialRoot:

Polynomial functions:

Rational functions:

Algebraic functions:

Addition:

Multiplication:

General expressions:

DifferentialRootReduce threads automatically overs lists:

DifferentialRootReduce can give non-homogeneous equations:

Use the option Method->"Homogeneous" to get an homogeneous equation: