What is the solution for (dy)/(dx)=(5y+8)^{2/3} ?

The solution for (dy)/(dx)=(5y+8)^{2/3} is y=(25(x^3+c_{1}^3)}{27}+\frac{25c_{1}x(x+c_{1}))/9-8/5

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(dy)/(dx)=(5y+8)^{2/3}

\frac{d y}{d x} = (5 y + 8)^{\frac{2}{3}}

y = \frac{25 ( x ^{3} + c _{1}^{3} )}{27} + \frac{25 c _{1} x ( x + c _{1} )}{9} - \frac{8}{5}

Solution steps

\frac{d y}{d x} = (5 y + 8)^{\frac{2}{3}}

Solve separable ODE:

y = \frac{25 ( x ^{3} + c _{1}^{3} )}{27} + \frac{25 c _{1} x ( x + c _{1} )}{9} - \frac{8}{5}

y = \frac{25 ( x ^{3} + c _{1}^{3} )}{27} + \frac{25 c _{1} x ( x + c _{1} )}{9} - \frac{8}{5}

\frac{d x}{d t} = 2 x + x

y^{^{'}} + \frac{t}{y ( t ^{2} - 1 )} = 0

e^{- x} \frac{d y}{d x} + x y = 0

\frac{d y}{d t} = - y a

y^{^{'}} = e^{9 x - 9 y}

What is the solution for (dy)/(dx)=(5y+8)^{2/3} ?
The solution for (dy)/(dx)=(5y+8)^{2/3} is y=(25(x^3+c_{1}^3)}{27}+\frac{25c_{1}x(x+c_{1}))/9-8/5