What is the solution for (dh)/(dt)=-3/100 sqrt(h-19) ?

The solution for (dh)/(dt)=-3/100 sqrt(h-19) is h=(9t^2+9c_{1}^2)/(40000)+(9c_{1}t)/(20000)+19

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(dh)/(dt)=-3/100 sqrt(h-19)

\frac{d h}{d t} = - \frac{3}{100} h - 19

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 19

Solution steps

\frac{d h}{d t} = - \frac{3}{100} h - 19

Solve separable ODE:

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 19

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 19

\frac{d x}{d t} = 50 - \frac{x}{100}, x = 3000, t = 0

f^{^{'}} (x) = f (x) (1 + x)

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

y^{^{'}} = y (e^{x} - x)

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

What is the solution for (dh)/(dt)=-3/100 sqrt(h-19) ?
The solution for (dh)/(dt)=-3/100 sqrt(h-19) is h=(9t^2+9c_{1}^2)/(40000)+(9c_{1}t)/(20000)+19