On the first integrals of the generalized Abel equation of the second kind of special form (Q905607)
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scientific article; zbMATH DE number 6533304
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the first integrals of the generalized Abel equation of the second kind of special form |
scientific article; zbMATH DE number 6533304 |
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On the first integrals of the generalized Abel equation of the second kind of special form (English)
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20 January 2016
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Consider the differential equation \[ \Biggl(\sum^{n-1}_{k=0} g_k(x) y^k\Biggr){dy\over dx}= \sum^n_{k=0} f_k(x) y^k,\qquad n\geq 2.\tag{\(*\)} \] The author derives conditions on the coefficient functions \(g_k\) and \(f_k\) for \((*)\) to find a first integral in explicit form.
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Abel equation of the second kind
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first integral
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