Finding Liouvillian first integrals of rational ODEs of any order in finite terms (Q2495216)
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| English | Finding Liouvillian first integrals of rational ODEs of any order in finite terms |
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Finding Liouvillian first integrals of rational ODEs of any order in finite terms (English)
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4 July 2006
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The author proposes an algebraic method for finding polynomials \(P_i,\) \(Q_j\) (without assumptions on their degrees) of the integrating factor \(\prod\limits_iP_i^{a_i}\exp(b_0\prod\limits_jQ_j^{b_j})\) of the differential equation \[ y^{(n)}(x)=\dfrac{A(x,y,y',\dots,y^{(n-1)})}{B(x,y,y',...,y^{(n-1)})} \] using the resultants of the polynomials \(A\) and \(B\).
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differential equations
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first integral
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exact solution
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