Concept

Ordinary differential equation

Summary
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. Differential equations 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 :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^{(n)}+b(x)=0, where a_0(x), ..., a_n(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y', \ldots, y^{(n)} are the successive derivatives of the unknown function y of the variable x. Among ordinary differential equations, linear differential equations play a prominent rol
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