What is the solution for (dy)/(dx)=((ln(x))^6)/(xy^2),y(1)=4 ?

The solution for (dy)/(dx)=((ln(x))^6)/(xy^2),y(1)=4 is y=\sqrt[3]{(3ln^7(x)+448)/7}

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(dy)/(dx)=((ln(x))^6)/(xy^2),y(1)=4

\frac{d y}{d x} = \frac{( ln ( x ) ) ^{6}}{x y ^{2}}, y (1) = 4

y = 3 \frac{3 ln ^{7} ( x ) + 448}{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 ) + 448}{7}

y = 3 \frac{3 ln ^{7} ( x ) + 448}{7}

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

\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

What is the solution for (dy)/(dx)=((ln(x))^6)/(xy^2),y(1)=4 ?
The solution for (dy)/(dx)=((ln(x))^6)/(xy^2),y(1)=4 is y=\sqrt[3]{(3ln^7(x)+448)/7}