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This will show how, in the case of an ordinary differential equation, the fact that the equation admits a continuous group of transformations may be taken advantage of for its integration.

Examples: d2z = g: ydx + xdy + zdz = 0. dt2 An ordinary differential equation involves only one independent variable, a partial differential equation involves more than one.

This result itself shows that every ordinary differential equation of the first order is subject to an infinite number of infinitesimal transformations.