How do you draw the slope field of the differential equation $\frac{d y}{d x} = \frac{1}{3} {(y - 1)}^{\frac{1}{3}}$ $dy/dx=1/3(y-1)^(1/3)$ ?

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How do you draw the slope field of the differential equation $\frac{d y}{d x} = \frac{1}{3} {(y - 1)}^{\frac{1}{3}}$ $dy/dx=1/3(y-1)^(1/3)$ ?

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Answer 1 · 2014-09-22T01:09:58

The first thing you need to do is solve the DE as separable equations:
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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 $\frac{3}{2}$ $3/2$ as the power. This means that the range can only be positive, so the slope field won't have any value below $y = 1$ $y=1$ .

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How do you draw the slope field of the differential equation $\frac{d y}{d x} = \frac{1}{3} {(y - 1)}^{\frac{1}{3}}$ $dy/dx=1/3(y-1)^(1/3)$ ?

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How do you draw the slope field of the differential equation $\frac{d y}{d x} = \frac{1}{3} {(y - 1)}^{\frac{1}{3}}$ $dy/dx=1/3(y-1)^(1/3)$ ?