Abel's theorem: Difference between revisions
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(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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[[Category:Differential Equations]] | [[Category:Differential Equations]] | ||
<math> | <math> | ||
\frac{dW}{dt}=pW | |||
</math> | </math> | ||
For [[Systems of ODEs]] | |||
<math> | <math> | ||
\frac{dW}{dt}=(p_{11}+p_{22}+\ldots+p_{nn})W=[trP]W | |||
</math> | </math> | ||
![{\displaystyle {\frac {dW}{dt}}=(p_{11}+p_{22}+\ldots +p_{nn})W=[trP]W}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d4f26039c15150732387b51098374d00581cc043)
