Solving Homogeneous ODEs of Class G
The general form of the homogeneous equation of class G is given by the following:
homogeneousG_ode := diff(y(x),x) = y(x)/x*F(y(x)/x^alpha);
where F is an arbitrary functions of its argument. 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 the homogeneousG_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