3.3.12 Homogeneous type G

This is what Maple calls this ode of this form

$$y^{\prime }=\frac{y}{x}F\left(\frac{y}{x^{\alpha }}\right)$$

The solution is implicit as

$$\ln x-c_1+{\int }^{y{x}^{\alpha }}\frac{1}{\tau (-\alpha -F\left(\tau \right))}d\tau =0$$

Lets look at some examples to better understand the method.