What is the solution for (dy)/(dx)=-8xy^2,y(0)=1 ?

The solution for (dy)/(dx)=-8xy^2,y(0)=1 is y= 1/(4x^2+1)

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(dy)/(dx)=-8xy^2,y(0)=1

\frac{d y}{d x} = - 8 x y^{2}, y (0) = 1

y = \frac{1}{4 x ^{2} + 1}

Solution steps

\frac{d y}{d x} = - 8 x y^{2}

Solve separable ODE:

y = \frac{1}{4 x ^{2} + 1}

y = \frac{1}{4 x ^{2} + 1}

y^{^{'}} = \frac{2 x}{1 + 2 y}, y (2) = - 0.2

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

y^{^{'}} = \frac{2 x}{1 + 2 y}, y (2) = - 0.5

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

(3 x y^{2} - 6 y) d x + (3 x^{2} y - 6 x) d y = 0

What is the solution for (dy)/(dx)=-8xy^2,y(0)=1 ?
The solution for (dy)/(dx)=-8xy^2,y(0)=1 is y= 1/(4x^2+1)