Linear homogeneous differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form

where ${\displaystyle a_{0}(x)}$, ..., ${\displaystyle a_{n}(x)}$ and ${\displaystyle b(x)}$ are arbitrary differentiable functions that do not need to be linear, and ${\displaystyle y',\ldots ,y^{n}}$ are the successive derivatives of an unknown function y of the variable x.

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