Notes on the Solutions of the First Order Quasilinear Differential Equations

Alena Vagaská, Dusan Mamrilla

Abstract


The system of the quasilinear differential first order equations with the antisymetric matrix and the same element f (t,x(t)) on the main diagonal have the property that r'(t) = f (t,x(t))r(t), where r(t) ≥ 0 is the po- lar function of the system. In special cases, when values f (t,x(t)) and g (t,x(t)) are only dependent on r^2 (t), t ∈ Jo we can find the general solution of the system (1) explicitly.


Keywords


nonlinear; quasilinear; differential equation; differential system;

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References


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DOI: http://dx.doi.org/10.23755/rm.v34i0.414

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.