What is the solution for (dx}{dt}=-\frac{50)/pi x^{-3/2} ?

The solution for (dx}{dt}=-\frac{50)/pi x^{-3/2} is x=((-125t-c_{1})/pi)^{2/5}

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(dx}{dt}=-\frac{50)/pi x^{-3/2}

\frac{d x}{d t} = - \frac{50}{π} x^{- \frac{3}{2}}

x = (\frac{- 125 t - c _{1}}{π})^{\frac{2}{5}}

Solution steps

\frac{d x}{d t} = - \frac{50}{π} x^{- \frac{3}{2}}

Solve separable ODE:

x = (\frac{- 125 t - c _{1}}{π})^{\frac{2}{5}}

x = (\frac{- 125 t - c _{1}}{π})^{\frac{2}{5}}

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What is the solution for (dx}{dt}=-\frac{50)/pi x^{-3/2} ?
The solution for (dx}{dt}=-\frac{50)/pi x^{-3/2} is x=((-125t-c_{1})/pi)^{2/5}