Solving d'Alembert ODEs - Maple Help

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Solving d'Alembert ODEs



The general form of the d'Alembert ODE is given by:

dAlembert_ode := y(x)=x*f(diff(y(x),x))+g(diff(y(x),x));



where f and g are arbitrary functions. See Differentialgleichungen, by E. Kamke, p. 31. This ODE is actually a generalization of the Clairaut ODE, and is almost always dealt with by looking for a solution in parametric form. For more information, see odeadvisor[patterns].








The general form of the solution for the d'Alembert ODE is returned by dsolve in parametric form, together with a possible singular solution, as follows:




See Also

DEtools, odeadvisor, dsolve, and ?odeadvisor,<TYPE> where <TYPE> is one of: quadrature, linear, separable, Bernoulli, exact, homogeneous, homogeneousB, homogeneousC, homogeneousD, homogeneousG, Chini, Riccati, Abel, Abel2A, Abel2C, rational, Clairaut, dAlembert, sym_implicit, patterns; for other differential orders see odeadvisor,types.

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