What is the solution for (dr)/(dx)= 4/3 pir^3 ?

The solution for (dr)/(dx)= 4/3 pir^3 is r=sqrt(-3/(8pi(x+c_{1)))},r=-sqrt(-3/(8pi(x+c_{1)))}

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(dr)/(dx)= 4/3 pir^3

\frac{d r}{d x} = \frac{4}{3} π r^{3}

r = - \frac{3}{8 π ( x + c _{1} )}, r = - - \frac{3}{8 π ( x + c _{1} )}

Solution steps

\frac{d r}{d x} = \frac{4}{3} π r^{3}

Solve separable ODE:

r = - \frac{3}{8 π ( x + c _{1} )}, r = - - \frac{3}{8 π ( x + c _{1} )}

r = - \frac{3}{8 π ( x + c _{1} )}, r = - - \frac{3}{8 π ( x + c _{1} )}

\frac{d y}{d x} = 5 x^{2} y - 9 x y

x y^{^{'}} + y - 6 = 0

y^{^{'}} = \frac{x ^{2} - 5}{y ^{2}}, y (0) = 3

x^{^{'}} = (x)^{22} (ln (t) + (10) + t e^{t})

y^{^{'}} = x y - x - y + 1

What is the solution for (dr)/(dx)= 4/3 pir^3 ?
The solution for (dr)/(dx)= 4/3 pir^3 is r=sqrt(-3/(8pi(x+c_{1)))},r=-sqrt(-3/(8pi(x+c_{1)))}