# 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 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

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- What is a solution to the differential equation #dy/dx=sqrt(xy)sinx#?

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