What is the solution for (dh)/(dt)=-2ksqrt(h) ?

The solution for (dh)/(dt)=-2ksqrt(h) is h=k^2t^2-c_{1}kt+(c_{1}^2)/4

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(dh)/(dt)=-2ksqrt(h)

\frac{d h}{d t} = - 2 k h

h = k^{2} t^{2} - c_{1} k t + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d h}{d t} = - 2 k h

Solve separable ODE:

h = k^{2} t^{2} - c_{1} k t + \frac{c _{1}^{2}}{4}

h = k^{2} t^{2} - c_{1} k t + \frac{c _{1}^{2}}{4}

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

\frac{d}{d A} (0.0155 A^{3} - 0.372 A^{2} + 3.95 A + 1.21)

\int_{- 3}^{- 1} \frac{1}{x} d x

x - \frac{1}{x}

What is the solution for (dh)/(dt)=-2ksqrt(h) ?
The solution for (dh)/(dt)=-2ksqrt(h) is h=k^2t^2-c_{1}kt+(c_{1}^2)/4