2.12 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

\[ \ln x-c_{1}+\int ^{yx^{\alpha }}\frac {1}{\tau \left ( -\alpha -F\left ( \tau \right ) \right ) }d\tau =0 \]

Lets look at some examples to better understand the method.