# How do you draw the slope field of the differential equation dy/dx=1/3(y-1)^(1/3) ?

Sep 22, 2014

The first thing you need to do is solve the DE as separable equations:

Normally slope fields are drawn by hand. There are many on-line plotters available. The one below is by MathScoop :

It's not obvious, unless you solve the separable equation. Looking at the RHS, you see $\frac{3}{2}$ as the power. This means that the range can only be positive, so the slope field won't have any value below $y = 1$.