What is the solution for (dh)/(dt)=-3/100 sqrt(h-16) ?

The solution for (dh)/(dt)=-3/100 sqrt(h-16) is h=(9t^2+9c_{1}^2)/(40000)+(9c_{1}t)/(20000)+16

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(dh)/(dt)=-3/100 sqrt(h-16)

\frac{d h}{d t} = - \frac{3}{100} h - 16

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 16

Solution steps

\frac{d h}{d t} = - \frac{3}{100} h - 16

Solve separable ODE:

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 16

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 16

\frac{d y}{d x} + x^{3} y = 2 x^{3}

3 x y^{^{'}} - 5 y = 0

x ln (x) = y (1 + 3 + y^{2}) y^{^{'}} (x), y (1) = 1

\frac{4 d y}{( x ^{2} + 1 ) d x} = \frac{1}{2 y}

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

What is the solution for (dh)/(dt)=-3/100 sqrt(h-16) ?
The solution for (dh)/(dt)=-3/100 sqrt(h-16) is h=(9t^2+9c_{1}^2)/(40000)+(9c_{1}t)/(20000)+16