What is the solution for (dx)/(dt)=2xsqrt(x) ?

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

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(dx)/(dt)=2xsqrt(x)

\frac{d x}{d t} = 2 x x

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

Solution steps

\frac{d x}{d t} = 2 x x

Solve separable ODE:

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

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

8 x \frac{d y}{d x} = - \frac{1}{y ^{3} 1 + x}

\frac{d y}{d t} + e^{t} y = 24 e^{t}

\frac{y d t}{d y} = t^{2} - 10 t + 21

\frac{d y}{d x} = \frac{y}{x ^{2} - 4}

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