The given problem for multiple differential equations (not in a system) is: "Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x(adsbygoogle = window.adsbygoogle || []).push({}); _{0},y_{0}) in the region."

I'm not entirely sure what to do with this. Looking at the function:

[tex]\frac{dy}{dx}=y^{\frac{2}{3}}[/tex]

I found the unknown function to be:

[tex]y=(\frac{x}{3})^3[/tex]

And I have verified that it is a solution.

Now the books says the answer is: "half-planes defined by either y>0 or y<0"

I'm not sure how this solution works. Could someone please explain it to me?

I also don't understand why y=0 isn't valid. I can see y=0 satisfying this equation:

0=0

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# Homework Help: DE Question

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