\[ y^{\prime }=f\left ( x,y\right ) \] ode internal name "homogeneousTypeD2"
These are ode of any form, in which the change of variables results in either separable or quadrature ode. Hence given an ode \(y^{\prime }=f\left ( x,y\right ) \) the change of variables \(y\left ( x\right ) =u\left ( x\right ) x\) is made and the resulting ode in \(u\left ( x\right ) \) is examined. If it is separable or quadrature, then it is solved for \(u\) and hence the solution \(y=ux\) is found.