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International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 1, Pages 143-145
Research notes

Alternative integration procedure for scale-invariant ordinary differential equations

Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA

Received 28 December 1978

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.


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.