What is the solution for (dh)/(dt)=-1/72 sqrt(h) ?

The solution for (dh)/(dt)=-1/72 sqrt(h) is h=(t^2)/(20736)+(c_{1}t)/(10368)+(c_{1}^2)/(20736)

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(dh)/(dt)=-1/72 sqrt(h)

\frac{d h}{d t} = - \frac{1}{72} h

h = \frac{t ^{2}}{20736} + \frac{c _{1} t}{10368} + \frac{c _{1}^{2}}{20736}

Solution steps

\frac{d h}{d t} = - \frac{1}{72} h

Solve separable ODE:

h = \frac{t ^{2}}{20736} + \frac{c _{1} t}{10368} + \frac{c _{1}^{2}}{20736}

h = \frac{t ^{2}}{20736} + \frac{c _{1} t}{10368} + \frac{c _{1}^{2}}{20736}

(y) sin (x) + y^{^{'}} = sin (x)

x^{2} y - 3 x y^{^{'}} - 2 y = 0

sin (x) d x + \frac{1}{y} d y = 0, y (0) = 0

\frac{d y}{d x} = x^{8} y^{- 5}, y (0) = 2

x^{2} \frac{d x}{d y} = e^{2}

What is the solution for (dh)/(dt)=-1/72 sqrt(h) ?
The solution for (dh)/(dt)=-1/72 sqrt(h) is h=(t^2)/(20736)+(c_{1}t)/(10368)+(c_{1}^2)/(20736)