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);
homogeneousB_ode ≔ F⁡ⅆⅆx⁢y⁡x,y⁡xx
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
ans ≔ dsolve⁡homogeneousB_ode
ans ≔ y⁡x=RootOf⁡−∫_Z1RootOf⁡F⁡_Z,_a−_aⅆ_a+ln⁡x+_C1⁢x
Explicit or implicit results can be tested, in principle, using odetest:
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