Friday, 25 July 2014

calculus - Why does 3x2+y3+9=2xy cannot be written in explicit form?



For this equation




3x2+y3+9=2xy,



I checked on wolfram alpha and it doesn't seem to have an explicit form where y is isolated and equals a function of x's only.



The problem is that I don't understand why it can't be written explicitly, as the graph of the relation is a [non injective] function : it doesn't have more than one value of y for each value of x.



So I should be able to write it as any normal function where y=f(x) and its derivative with respect to x should be expressed with only x's instead of x's and y's - its derivative is : 2(3x+y)3y2+2x.



Please illuminate me, i'm really clueless.


Answer




According to wolfram alpha, there does exist a real explicit form:



enter image description here


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