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].