What is the solution for y^'=10x^3y^7 ?

The solution for y^'=10x^3y^7 is y=\sqrt[6]{-1/(3(5x^4+c_{1))}},y=-\sqrt[6]{-1/(3(5x^4+c_{1))}}

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y^'=10x^3y^7

y^{^{'}} = 10 x^{3} y^{7}

Solution steps

y^{'} (x) = 10 x^{3} y^{7}

Solve separable ODE:

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9 x^{3} y^{2} \frac{d y}{d x} = - 9 x^{2} y^{3}

\frac{d y}{d x} = \frac{cot ( x )}{y}, y (\frac{π}{2}) = 0

x y^{^{'}} - (1 + x^{2}) y = 0

What is the solution for y^'=10x^3y^7 ?
The solution for y^'=10x^3y^7 is y=\sqrt[6]{-1/(3(5x^4+c_{1))}},y=-\sqrt[6]{-1/(3(5x^4+c_{1))}}