International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1979 / Article

Research notes | Open Access

Volume 2 |Article ID 282618 | https://doi.org/10.1155/S0161171279000144

Gerald Rosen, "Alternative integration procedure for scale-invariant ordinary differential equations", International Journal of Mathematics and Mathematical Sciences, vol. 2, Article ID 282618, 3 pages, 1979. https://doi.org/10.1155/S0161171279000144

Alternative integration procedure for scale-invariant ordinary differential equations

Received28 Dec 1978

Abstract

For an ordinary differential equation invariant under a one-parameter group of scale transformations xλx, yλαy, yλα1y, yλα2y, etc., it is shown by example that an explicit analytical general solution may be obtainable in parametric form in terms of the scale-invariant variable ξ=xy1/αdx. This alternative integration may go through, as it does for the example equation y=kxy2y, in cases for which the customary dependent and independent variables (xαy) and (nx) do not yield an analytically integrable transformed equation.

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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