What is the solution for (dr)/(dt)=-r^3 ?

The solution for (dr)/(dt)=-r^3 is r=sqrt(-1/(2(-t+c_{1)))},r=-sqrt(-1/(2(-t+c_{1)))}

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(dr)/(dt)=-r^3

\frac{d r}{d t} = - r^{3}

r = - \frac{1}{2 ( - t + c _{1} )}, r = - - \frac{1}{2 ( - t + c _{1} )}

Solution steps

\frac{d r}{d t} = - r^{3}

Solve separable ODE:

r = - \frac{1}{2 ( - t + c _{1} )}, r = - - \frac{1}{2 ( - t + c _{1} )}

r = - \frac{1}{2 ( - t + c _{1} )}, r = - - \frac{1}{2 ( - t + c _{1} )}

1600 y^{^{''}} - 9 y = 0, y (0) = 7, y^{^{'}} (0) = 6

x \to - 1 lim (x^{2} + 4 x)

\frac{d y}{d t} = 4 y + y^{4}

f (x) = - \frac{4 x}{x ^{2} + 1}, at x = 0

\int r^{2} (\frac{r ^{3}}{15} - 8)^{4} d r

What is the solution for (dr)/(dt)=-r^3 ?
The solution for (dr)/(dt)=-r^3 is r=sqrt(-1/(2(-t+c_{1)))},r=-sqrt(-1/(2(-t+c_{1)))}