What is the solution for y^'=((ln(x))^3)/(xy^2) ?

The solution for y^'=((ln(x))^3)/(xy^2) is y=\sqrt[3]{(3ln^4(x)+c_{1})/4}

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y^'=((ln(x))^3)/(xy^2)

y^{^{'}} = \frac{( ln ( x ) ) ^{3}}{x y ^{2}}

y = 3 \frac{3 ln ^{4} ( x ) + c _{1}}{4}

Solution steps

y^{'} (x) = \frac{( ln ( x ) ) ^{3}}{x y ^{2}}

Solve separable ODE:

y = 3 \frac{3 ln ^{4} ( x ) + c _{1}}{4}

y = 3 \frac{3 ln ^{4} ( x ) + c _{1}}{4}

\frac{d}{d x} ((y)^{2}) + \frac{d y}{d x} - 2 y = 0

y^{^{'}} + x y = 5 x y^{2}

\frac{x}{y} = \frac{d y}{d x}

y^{^{'}} = e^{y}, y (0) = 0

2 x^{3} H (x) (x)^{2} d x + x^{4} H (x) d H (x) = 0

What is the solution for y^'=((ln(x))^3)/(xy^2) ?
The solution for y^'=((ln(x))^3)/(xy^2) is y=\sqrt[3]{(3ln^4(x)+c_{1})/4}