What is the solution for (dx)/(dt)=tx^{1/3},x(1)=1 ?

The solution for (dx)/(dt)=tx^{1/3},x(1)=1 is x=(sqrt(t^6+8+6t^4+12t^2))/(3sqrt(3))

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(dx)/(dt)=tx^{1/3},x(1)=1

\frac{d x}{d t} = t x^{\frac{1}{3}}, x (1) = 1

x = \frac{t ^{6} + 8 + 6 t ^{4} + 12 t ^{2}}{3 3}

Solution steps

\frac{d x}{d t} = t x^{\frac{1}{3}}

Solve separable ODE:

x = \frac{t ^{6} + 8 + 6 t ^{4} + 12 t ^{2}}{3 3}

x = \frac{t ^{6} + 8 + 6 t ^{4} + 12 t ^{2}}{3 3}

\int_{0}^{4} \frac{x}{9 + x ^{2}} d x

\frac{d}{d x} (10 x^{2} e^{x})

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x

\frac{d y}{d x} = (y + 5) (x + 2)

\frac{d}{d x} (- \frac{x}{10})

What is the solution for (dx)/(dt)=tx^{1/3},x(1)=1 ?
The solution for (dx)/(dt)=tx^{1/3},x(1)=1 is x=(sqrt(t^6+8+6t^4+12t^2))/(3sqrt(3))