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

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

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(ln(y))^2(dy)/(dx)=x^2y,y(1)=e^2

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

Solution steps

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

Solve separable ODE:

x (x z) + (x z)^{2} d x - x^{2} (x d z + z d x) = 0

2 x y d x = (2 - x^{2}) d y

(u y + y) (u d y + y d u) - u y d y = 0

\frac{d y}{d x} = - \frac{5}{3} x^{9} y^{8}

\frac{d x}{d t} = a - b x^{2}

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