What is the solution for (dy)/(dx)=((ln(x))^6)/(xy^2) ?

The solution for (dy)/(dx)=((ln(x))^6)/(xy^2) is y=\sqrt[3]{(3ln^7(x)+c_{1})/7}

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(dy)/(dx)=((ln(x))^6)/(xy^2)

\frac{d y}{d x} = \frac{( ln ( x ) ) ^{6}}{x y ^{2}}

y = 3 \frac{3 ln ^{7} ( x ) + c _{1}}{7}

Solution steps

\frac{d y}{d x} = \frac{( ln ( x ) ) ^{6}}{x y ^{2}}

Solve separable ODE:

y = 3 \frac{3 ln ^{7} ( x ) + c _{1}}{7}

y = 3 \frac{3 ln ^{7} ( x ) + c _{1}}{7}

(e^{y} - 1) \frac{d y}{d x} = 2 + cos (x)

y^{^{'}} + 5 y^{3} = 0

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

y^{'} (t) = y (y + 1)^{2}, y (0) = 1

\frac{d x}{d t} = x^{2} e^{- 2 t}

What is the solution for (dy)/(dx)=((ln(x))^6)/(xy^2) ?
The solution for (dy)/(dx)=((ln(x))^6)/(xy^2) is y=\sqrt[3]{(3ln^7(x)+c_{1})/7}