Solving Homogeneous ODEs of Class B
The general form of the homogeneous equation of class B is given by the following:
homogeneousB_ode := F(diff(y(x),x), y(x)/x);
where F is an arbitrary functions of its arguments. See Differentialgleichungen, by E. Kamke, p. 19. 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 homogeneousB_ode
The general solution for this ODE
Explicit or implicit results can be tested, in principle, using odetest:
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.
Download Help Document