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

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

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(dx)/(dt)=sqrt(x)

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

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

Solution steps

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

Solve separable ODE:

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

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

(ln (x - 1))^{^{'}}

t an g e n t y = \frac{x}{( 1 + x ^{2} )}

\int_{- \infty}^{3} \frac{1}{4 + x ^{2}} d x

d er i v a t i v e f (x) = e^{9 x} + 9 e^{9 x} x

\int \frac{1}{( x ^{2} + 4 ) ^{2}} d x

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