What is the solution for (ln(y))^3(dy)/(dx)=x^3y ?

The solution for (ln(y))^3(dy)/(dx)=x^3y is y=e^{\sqrt[4]{x^4+c_{1}}},y=e^{-\sqrt[4]{x^4+c_{1}}}

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(ln(y))^3(dy)/(dx)=x^3y

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

y = e^{4 x^{4} + c_{1}}, y = e^{- 4 x^{4} + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{4 x^{4} + c_{1}}, y = e^{- 4 x^{4} + c_{1}}

y = e^{4 x^{4} + c_{1}}, y = e^{- 4 x^{4} + c_{1}}

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

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

e^{2 x} y^{^{'}} = y - y e^{3 x}

(t^{2} - 16 t + 48) \frac{d y}{d t} = y

y^{^{'}} = 6 y - 15

What is the solution for (ln(y))^3(dy)/(dx)=x^3y ?
The solution for (ln(y))^3(dy)/(dx)=x^3y is y=e^{\sqrt[4]{x^4+c_{1}}},y=e^{-\sqrt[4]{x^4+c_{1}}}