1. Integrating factor of a 1-form

Giving a Frobenius integrable 1-form ω necessarily there exist a smooth function F and a non vanishing smooth function μ such that $$

dF=\mu \omega.

$$

En tal caso, μ recibe el nombre de integrating factor y F es una first integral of the Pfaffian system S(ω). Tiene relación inversa con las symmetrising factors.

2. Integrating factor of an ODE

Given an ODE Δ, we call integrating factor of Δ to any non vanishing smooth function μ∈Jm (the jet bundle) such that

Dx(F)=μΔ

for a smooth function F called first integral.

To see the relation between integrating factor of an ODE and the integrating factor of the associated 1-form go to the note first integral#3 b First integal of an m th-order ODE.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es


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