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);
homogeneousG_ode ≔ ⅆⅆx⁢y⁡x=y⁡x⁢F⁡y⁡xxαx
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
ans ≔ dsolve⁡homogeneousG_ode
ans ≔ y⁡x=RootOf⁡−ln⁡x+_C1+∫_Z1_a⁢−α+F⁡_aⅆ_a⁢xα
Explicit or implicit results can be tested, in principle, using odetest
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