Abel's theorem

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Revision as of 19:05, 19 May 2024 by Rice (talk | contribs) (Created page with "Category:Differential Equations '''Abel's theorem''' in linear differential equations states that for any second order linear homogeneous ODE, <math> y'' + p(t)y'+q(t)y=0 </math> Given <math>y_1, y_2</math> as particular solutions to the ODE, then the Wronskian of the two solutions can be described in terms of the ODE's coefficients as <math> W(t)=Ce^{\int p(x)dx} </math>")
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Abel's theorem in linear differential equations states that for any second order linear homogeneous ODE,

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y''+p(t)y'+q(t)y=0}

Given Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_1, y_2} as particular solutions to the ODE, then the Wronskian of the two solutions can be described in terms of the ODE's coefficients as

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W(t)=Ce^{\int p(x)dx} }