What is the solution for (dx)/(dt)=t*x^{1/2} ?

The solution for (dx)/(dt)=t*x^{1/2} is x=(t^4}{16}+\frac{c_{1}t^2)/4+(c_{1}^2)/4

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(dx)/(dt)=t*x^{1/2}

\frac{d x}{d t} = t \cdot x^{\frac{1}{2}}

x = \frac{t ^{4}}{16} + \frac{c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d x}{d t} = t \cdot x^{\frac{1}{2}}

Solve separable ODE:

x = \frac{t ^{4}}{16} + \frac{c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4}

x = \frac{t ^{4}}{16} + \frac{c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4}

What is the solution for (dx)/(dt)=t*x^{1/2} ?
The solution for (dx)/(dt)=t*x^{1/2} is x=(t^4}{16}+\frac{c_{1}t^2)/4+(c_{1}^2)/4