What is the solution for derivative of (x^8/(y^5))=0 ?

The solution for derivative of (x^8/(y^5))=0 is y=(x\sqrt[5]{x^3})/(c_{1)}

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derivative of (x^8/(y^5))=0

\frac{d}{d x} (\frac{x ^{8}}{y ^{5}}) = 0

y = \frac{x 5 x ^{3}}{c _{1}}

Solution steps

\frac{d}{d x} (\frac{x ^{8}}{y ^{5}}) = 0

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

\frac{x ^{8}}{y ^{5}} = \int 0 d x

\int 0 d x = c_{1}

\frac{x ^{8}}{y ^{5}} = c_{1}

Isolate

y : y = \frac{x 5 x ^{3}}{5 c _{1}}

y = \frac{x 5 x ^{3}}{5 c _{1}}

Simplify

y = \frac{x 5 x ^{3}}{c _{1}}

y^{^{'}} = (\frac{1}{1 + x}) y

y = \frac{3 ( 1 + 3 x ^{2} ) ^{2}}{x} \frac{d y}{d x}

\frac{d y}{d t} y = 3 + csc (t^{6})

6 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = - 5

6 u z^{2} d u = u d z

What is the solution for derivative of (x^8/(y^5))=0 ?
The solution for derivative of (x^8/(y^5))=0 is y=(x\sqrt[5]{x^3})/(c_{1)}