What is the solution for (dh)/(dt)=5sqrt(h) ?

The solution for (dh)/(dt)=5sqrt(h) is h=(25t^2)/4+(5c_{1}t)/2+(c_{1}^2)/4

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(dh)/(dt)=5sqrt(h)

\frac{d h}{d t} = 5 h

h = \frac{25 t ^{2}}{4} + \frac{5 c _{1} t}{2} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d h}{d t} = 5 h

Solve separable ODE:

h = \frac{25 t ^{2}}{4} + \frac{5 c _{1} t}{2} + \frac{c _{1}^{2}}{4}

h = \frac{25 t ^{2}}{4} + \frac{5 c _{1} t}{2} + \frac{c _{1}^{2}}{4}

1 + x^{2} d y - 1 - y^{2} d x = 0

\int (13 x + 3) d x

x^{a}

\frac{d}{d t} (tan (5 t))

What is the solution for (dh)/(dt)=5sqrt(h) ?
The solution for (dh)/(dt)=5sqrt(h) is h=(25t^2)/4+(5c_{1}t)/2+(c_{1}^2)/4