What is the solution for (dh)/(dt)=-3/100 sqrt(h-20) ?

The solution for (dh)/(dt)=-3/100 sqrt(h-20) is h=(9t^2+9c_{1}^2)/(40000)+(9c_{1}t)/(20000)+20

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(dh)/(dt)=-3/100 sqrt(h-20)

\frac{d h}{d t} = - \frac{3}{100} h - 20

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 20

Solution steps

\frac{d h}{d t} = - \frac{3}{100} h - 20

Solve separable ODE:

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 20

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 20

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

x \frac{d y}{d x} + y^{2} = 1

\frac{d x}{d t} = 60 - \frac{x}{100}, x = 2000, t = 0

x y^{2} cos (x) d x - 3 x^{2} y cos (x) d y = 0

\frac{d y}{d x} - y (6 x + 1) = 0

What is the solution for (dh)/(dt)=-3/100 sqrt(h-20) ?
The solution for (dh)/(dt)=-3/100 sqrt(h-20) is h=(9t^2+9c_{1}^2)/(40000)+(9c_{1}t)/(20000)+20