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

2 y^{^{'}} = e^{2 x} y^{4}

\frac{d x}{d t} = 1 - \frac{x}{25}

(1 + cos (x)) \frac{d y}{d x} = sin (x) (e - y + 1)

x \frac{d t}{d x} = \frac{a + a t ^{2}}{1 - a t}

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