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QUESTION
How do you draw the slope field of the differential equation ##dy/dx=1/3(y-1)^(1/3)## ?
The first thing you need to do is solve the DE as separable equations:
Normally 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 ##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##.
