Reducing \(y''=F(x,y,y')\) to first order. (Q1811598)
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scientific article; zbMATH DE number 1929363
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reducing \(y''=F(x,y,y')\) to first order. |
scientific article; zbMATH DE number 1929363 |
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Reducing \(y''=F(x,y,y')\) to first order. (English)
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17 June 2003
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The authors study the second-order ODE (1) \(y'' = F(x, y, y')\). They show that by the transformations \(\bar x = \phi (x)\), \(\bar y = \psi (x, y)\), equation (1) can be reduced to a first-order equation of the form \(z' = f(\bar x, z),\) where \(z=\frac{d\bar y}{d \bar x}, z' = \frac{dz}{d \bar x}.\) Some examples and particular cases are discussed.
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complete integrability
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fibred automorphism
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jet bundle
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order reduction
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second-order ODE
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