The general form of the homogeneous equation of class C is given by the following:

homogeneousC_ode := diff(y(x),x)=F((a*x+b*y(x)+c)/(r*x+s*y(x)+t));

$\mathrm{homogeneousC\_ode}≔\frac{\ⅆ}{\ⅆx}y\left(x\right)=F\left(\frac{ax+by\left(x\right)+c}{rx+sy\left(x\right)+t}\right)$

where F is an arbitrary function of its argument. 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.

with(DEtools, odeadvisor, symgen);

$\left[\mathrm{odeadvisor}\,\mathrm{symgen}\right]$

odeadvisor(homogeneousC_ode);

$\left[\left[\mathrm{\_homogeneous}\,\mathrm{class\; C}\right]\,\mathrm{\_dAlembert}\right]$

symgen(homogeneousC_ode);

$\left[\mathrm{\_\ξ}=\frac{asx-brx-bt+cs}{as-br}\,\mathrm{\_\η}=\frac{asy-bry+at-cr}{as-br}\right]$

ans := dsolve(homogeneousC_ode);

odetest(ans,homogeneousC_ode);

$0$