3.3.11 Homogeneous type D2

$$y^{\prime }=f(x,y)$$

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 $y^{\prime }=f(x,y)$ 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.