: Mathématiques: linear differential equation

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linear 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 ${\\displaystyle a_{0}(x)y+a_{1}(x)y'+a_{2}(x)y''\\cdots +a_{n}(x)y^{(n)}=b(x)}$ where $a 0 (x)$ , ..., $a n (x)$ and $b (x)$ are arbitrary differentiable functions that do not need to be linear, and $y', ..., y (n)$ are the successive derivatives of an unknown function $y$ of the variable $x$ . Such an equation is an ordinary differential equation (ODE). A linear differential equation may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Linear_differential_equation)

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