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

1 Answer
Sep 22, 2014

The first thing you need to do is solve the DE as separable equations:
enter image source here

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

It's not obvious, unless you solve the separable equation. Looking at the RHS, you see #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#.