# What is a homogeneous equation function

Definitions

Definition: homogeneous functions | |

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Explanation and examples | |

A function f (x, y) is homogeneous if it can be written as a product, where one factor is a power of x and the other factor is a function of y / x (i.e. a function whose argument is y / x). In the example y / x the argument of the sine function: In this example, y / x is the argument of the power function: The function of y / x can consist of several sub-functions, in the example from the sine function and an exponential function: The power of x can also be x ^{0}= 1, i.e. omitted. The degree of homogeneity is then zero: The second factor can also be a function of x / y instead of y / x, because you can always write x / y as a double fraction: | |

Recognizing the homogeneity by factoring out | |

Particularly in the case of completely rational functions, the homogeneity can only be recognized when if one excludes a power of x. example On the next page we will therefore specify a rule that allows you to do without previous bracketing can very easily check whether a completely rational function is homogeneous and what degree of homogeneity has, i.e. what power x ^{n} mancan exclude. | |

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