What is the solution for (dy)/(dx)=x^2y^{-7} ?

The solution for (dy)/(dx)=x^2y^{-7} is y=\sqrt[8]{(8x^3)/3+c_{1}},y=-\sqrt[8]{(8x^3)/3+c_{1}}

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(dy)/(dx)=x^2y^{-7}

\frac{d y}{d x} = x^{2} y^{- 7}

y = 8 \frac{8 x ^{3}}{3} + c_{1}, y = - 8 \frac{8 x ^{3}}{3} + c_{1}

Solution steps

\frac{d y}{d x} = x^{2} y^{- 7}

Solve separable ODE:

y = 8 \frac{8 x ^{3}}{3} + c_{1}, y = - 8 \frac{8 x ^{3}}{3} + c_{1}

y = 8 \frac{8 x ^{3}}{3} + c_{1}, y = - 8 \frac{8 x ^{3}}{3} + c_{1}

(x - 2) y^{^{'}} = 3 y

y^{^{'}} sec (x) = 5 y^{2}, y (\frac{9 π}{2}) = \frac{1}{6}

\frac{d y}{d x} = \frac{3}{y ^{2}}

3 y x + y^{^{'}} = 3 x y^{2}

\frac{d y}{d x} y = - \frac{2}{3 x ^{4}}

What is the solution for (dy)/(dx)=x^2y^{-7} ?
The solution for (dy)/(dx)=x^2y^{-7} is y=\sqrt[8]{(8x^3)/3+c_{1}},y=-\sqrt[8]{(8x^3)/3+c_{1}}