What is the solution for (dy)/(dx)=8x^4(6+y^2)^{3/2} ?

The solution for (dy)/(dx)=8x^4(6+y^2)^{3/2} is

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(dy)/(dx)=8x^4(6+y^2)^{3/2}

\frac{d y}{d x} = 8 x^{4} (6 + y^{2})^{\frac{3}{2}}

y = \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}, y = - \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}

Solution steps

\frac{d y}{d x} = 8 x^{4} (6 + y^{2})^{\frac{3}{2}}

Solve separable ODE:

y = \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}, y = - \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}

y = \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}, y = - \frac{6 6 - 64 x ^{10} - 80 c _{1} x ^{5} - 25 c _{1}^{2}}{- 25 + 900 c _{1}^{2} + 2880 c _{1} x ^{5} + 2304 x ^{10}}

x \to 0 lim (\frac{e ^{x} - 1}{5 x})

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

\int \frac{9 x}{x ^{3} + 1} d x

\frac{\partial}{\partial x} (2 - (x^{2} + y^{2})^{\frac{1}{7}})

y = (x^{5} - 1)^{3}

What is the solution for (dy)/(dx)=8x^4(6+y^2)^{3/2} ?
The solution for (dy)/(dx)=8x^4(6+y^2)^{3/2} is