What is the solution for (dy)/(dx)+4xy^3=0,y(0)= 1/2 ?

The solution for (dy)/(dx)+4xy^3=0,y(0)= 1/2 is y= 1/(2sqrt(x^2+1))

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(dy)/(dx)+4xy^3=0,y(0)= 1/2

\frac{d y}{d x} + 4 x y^{3} = 0, y (0) = \frac{1}{2}

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

Solution steps

\frac{d y}{d x} + 4 x y^{3} = 0

Solve separable ODE:

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

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

\frac{d y}{d t} = - k y + 100 k, y (0) = 50

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

t x^{^{'}} = - t^{2} x^{3}

x^{^{'}} = x (t^{2} - 1) (t^{2} - 9), x (0) = 1

y^{^{'}} = \frac{t ( 4 y - y ^{2} )}{3}

What is the solution for (dy)/(dx)+4xy^3=0,y(0)= 1/2 ?
The solution for (dy)/(dx)+4xy^3=0,y(0)= 1/2 is y= 1/(2sqrt(x^2+1))