Crazy diffy!

Calculus Level 5

\[\dfrac { { d }^{ 2 }x }{ { dy }^{ 2 } } =\dfrac { 1 }{ 3 } \sqrt { 1+{ \left( \dfrac { dx }{ dy } \right) }^{ 2 } } \]

Consider the differential equation above. You are given that if \(y = 0\), then \(x=3\) and \(\dfrac{dx}{dy} = 0\) when \(x=0\).

Find the value of \(x\) when \(y = 6\).

If the value you've found is \(z\), submit the answer as \(\lfloor z \rfloor \).

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