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

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

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

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

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

Solution steps

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

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}

f (5)

5 cos (x), 5 cos (2 x), [0, π]

\int \frac{cos ^{5} ( 3 x )}{sin ^{14} ( 3 x )} d x

\frac{x - 1}{x ^{2}}

sin (\frac{t}{t + 4})

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