Solving Homogeneous ODEs of Class D
The general form of the homogeneous equation of class D is given by the following:
homogeneousD_ode := diff(y(x),x)= y(x)/x+g(x)*f(y(x)/x);
where f(y(x)/x) and g(x) are arbitrary functions of their arguments. See Differentialgleichungen, by E. Kamke, p. 20. This type of ODE can be solved in a general manner by dsolve and the coefficients of the infinitesimal symmetry generator are also found by symgen.
A pair of infinitesimals for homogeneousD_ode
The general solution for this ODE
ans ≔ dsolve⁡homogeneousD_ode
Answers can be tested using odetest
Let's see how the answer above works when turning f into an explicit function; f is the identity mapping.
f ≔ u→u
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