Research notes | Open Access
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
For an ordinary differential equation invariant under a one-parameter group of scale transformations , , , , 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 . This alternative integration may go through, as it does for the example equation , in cases for which the customary dependent and independent variables and do not yield an analytically integrable transformed equation.
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