# 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.

# Examples

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## Basic Examples(1)

Reduce the Bessel function to a DifferentialRoot:

## Scope(7)

Polynomial functions:

Rational functions:

Algebraic functions:

Multiplication:

General expressions:

## Options(1)

### Method(1)

DifferentialRootReduce can give non-homogeneous equations:

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

## Applications(3)

Use DifferentialRootReduce to generate the differential equations with initial values for elementary functions:

Use DifferentialRootReduce to generate the differential equations with initial values for special functions:

Use DifferentialRootReduce to generate the differential equations that obey combinations of different functions:

Wolfram Research (2008), DifferentialRootReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/DifferentialRootReduce.html (updated 2020).

#### Text

Wolfram Research (2008), DifferentialRootReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/DifferentialRootReduce.html (updated 2020).

#### CMS

Wolfram Language. 2008. "DifferentialRootReduce." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/DifferentialRootReduce.html.

#### APA

Wolfram Language. (2008). DifferentialRootReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DifferentialRootReduce.html

#### BibTeX

@misc{reference.wolfram_2022_differentialrootreduce, author="Wolfram Research", title="{DifferentialRootReduce}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/DifferentialRootReduce.html}", note=[Accessed: 28-March-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_differentialrootreduce, organization={Wolfram Research}, title={DifferentialRootReduce}, year={2020}, url={https://reference.wolfram.com/language/ref/DifferentialRootReduce.html}, note=[Accessed: 28-March-2023 ]}