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- Abels_identity abstract ""Abel's formula" redirects here. For the formula on difference operators, see Summation by parts.In mathematics, Abel's identity (also called Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation.The relation can be generalised to nth-order linear ordinary differential equations. The identity is named after the Norwegian mathematician Niels Henrik Abel.Since Abel's identity relates the different linearly independent solutions of the differential equation, it can be used to find one solution from the other. It provides useful identities relating the solutions, and is also useful as a part of other techniques such as the method of variation of parameters. It is especially useful for equations such as Bessel's equation where the solutions do not have a simple analytical form, because in such cases the Wronskian is difficult to compute directly.A generalisation to first-order systems of homogeneous linear differential equations is given by Liouville's formula.".
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- Abels_identity wikiPageWikiLink American_Mathematical_Society.
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- Abels_identity wikiPageWikiLink Chain_rule.
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- Abels_identity wikiPageWikiLink Exponential_function.
- Abels_identity wikiPageWikiLink Fundamental_theorem_of_calculus.
- Abels_identity wikiPageWikiLink Homogeneous_differential_equation.
- Abels_identity wikiPageWikiLink Interval_(mathematics).
- Abels_identity wikiPageWikiLink Leibniz_formula_for_determinants.
- Abels_identity wikiPageWikiLink Linear_independence.
- Abels_identity wikiPageWikiLink Liouvilles_formula.
- Abels_identity wikiPageWikiLink Mathematician.
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- Abels_identity wikiPageWikiLink Mean_value_theorem.
- Abels_identity wikiPageWikiLink Method_of_variation_of_parameters.
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- Abels_identity wikiPageWikiLink Product_rule.
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- Abels_identity wikiPageWikiLink Real_line.
- Abels_identity wikiPageWikiLink Real_number.
- Abels_identity wikiPageWikiLink Summation_by_parts.
- Abels_identity wikiPageWikiLink Trace_(linear_algebra).
- Abels_identity wikiPageWikiLink Variation_of_parameters.
- Abels_identity wikiPageWikiLink Wronskian.
- Abels_identity wikiPageWikiLinkText "Abel's identity".
- Abels_identity hasPhotoCollection Abels_identity.
- Abels_identity title "Abel's Differential Equation Identity".
- Abels_identity urlname "AbelsDifferentialEquationIdentity".
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- Abels_identity subject Category:Articles_containing_proofs.
- Abels_identity subject Category:Mathematical_identities.
- Abels_identity subject Category:Niels_Henrik_Abel.
- Abels_identity subject Category:Ordinary_differential_equations.
- Abels_identity comment ""Abel's formula" redirects here. For the formula on difference operators, see Summation by parts.In mathematics, Abel's identity (also called Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation.The relation can be generalised to nth-order linear ordinary differential equations.".
- Abels_identity label "Abel's identity".
- Abels_identity sameAs متطابقة_أبيل.
- Abels_identity sameAs Identitat_abeliana.
- Abels_identity sameAs Abelsche_Identität.
- Abels_identity sameAs Identidad_de_Abel.
- Abels_identity sameAs זהות_אבל.
- Abels_identity sameAs Identità_di_Abel.
- Abels_identity sameAs m.091yty.
- Abels_identity sameAs Q318714.
- Abels_identity sameAs Q318714.
- Abels_identity wasDerivedFrom Abels_identityoldid=605426991.
- Abels_identity isPrimaryTopicOf Abels_identity.