What is the solution for (dx)/(dt)=3sqrt(xt) ?

The solution for (dx)/(dt)=3sqrt(xt) is x=t^3+c_{1}t^{3/2}+(c_{1}^2)/4

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(dx)/(dt)=3sqrt(xt)

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

x = t^{3} + c_{1} t^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

x = t^{3} + c_{1} t^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

x = t^{3} + c_{1} t^{\frac{3}{2}} + \frac{c _{1}^{2}}{4}

x \to 1 lim (3 x^{2} + 2 x)

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n = 0 \sum \infty \frac{n}{( 2 n + 1 ) !}

f (x) = 9 x^{2} - x^{3}, at x = 2

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What is the solution for (dx)/(dt)=3sqrt(xt) ?
The solution for (dx)/(dt)=3sqrt(xt) is x=t^3+c_{1}t^{3/2}+(c_{1}^2)/4