differential equation: Quick Facts

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A graph of the function x equals A cosine omega t, showing a cosine wave oscillating between A and negative A along the vertical axis, with horizontal axis marked at pi and 2 pi.

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Topics

Bessel’s equation linear differential equation second-order differential equation initial value order dynamical systems theory homogeneous differential equation degree exact equation ordinary differential equation algebraic equation integral equation parametric equation quadratic equation linear equation discriminant difference equation system of equations

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Key People

Paul Painlevé.

Paul Painlevé

French prime minister and mathematician

Sophus Lie, detail of an engraving c. 1885.

Sophus Lie

Norwegian mathematician

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Joseph Bertrand

French mathematician and educator