What is the solution for -(dh)/(dt)=kh(t)^n ?

The solution for -(dh)/(dt)=kh(t)^n is h=e^{-(kt^{n+1})/(n+1)+c_{1}}

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-(dh)/(dt)=kh(t)^n

- \frac{d h}{d t} = kh (t)^{n}

h = e^{- \frac{k t ^{n + 1}}{n + 1} + c_{1}}

Solution steps

- \frac{d h}{d t} = kh t^{n}

Solve separable ODE:

h = e^{- \frac{k t ^{n + 1}}{n + 1} + c_{1}}

h = e^{- \frac{k t ^{n + 1}}{n + 1} + c_{1}}

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

\frac{d y}{d x} y = sin^{3} (cos (9 x))

\frac{d y}{d t} 400 = - \frac{π}{9} \cdot 8 y

\frac{d y}{d x} = 85 y x^{16}, y = 4

\frac{1}{x} \frac{d y}{d x} = 2 - 4 y

What is the solution for -(dh)/(dt)=kh(t)^n ?
The solution for -(dh)/(dt)=kh(t)^n is h=e^{-(kt^{n+1})/(n+1)+c_{1}}