Abstract
An ordinary differential equation (ODE) of order n has a general solution (excluding singular solutions) which depends on n arbitrary constants of integration. In the case of partial differential equations (PDE) the situation is more complicated. The general solution of a PDE does not depend on arbitrary constants, but on arbitrary functions. In general (excluding again the case of singular solutions), the number of these arbitrary functions is equal to the order of the equation. The arbitrary functions depend on one variable less than the solution itself.
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© 2002 Springer-Verlag Berlin Heidelberg
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Chattot, JJ. (2002). Partial Differential Equations. In: Computational Aerodynamics and Fluid Dynamics. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05064-4_4
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DOI: https://doi.org/10.1007/978-3-662-05064-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07798-2
Online ISBN: 978-3-662-05064-4
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