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}

\frac{d y}{d x} = \frac{cos ^{2} ( y )}{4 x - 3}

\frac{d p}{d t} = 5 p (20 - ln (p))

\frac{d y}{d x} + 2 x yy = 0, y (0) = - 1

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

y^{^{'}} - 3 y = 12, y (0) = 0

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