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

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

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(dy)/(dx)=xy^3(1+x^2)^{-1/2},y(0)=1

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

y = - \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{1}{2}} - 3}

Solution steps

\frac{d y}{d x} = x y^{3} (1 + x^{2})^{- \frac{1}{2}}

Solve separable ODE:

y = - \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{1}{2}} - 3}

y = - \frac{1}{2 ( x ^{2} + 1 ) ^{\frac{1}{2}} - 3}

\frac{\partial}{\partial x} (- x y (- 15 - x - y))

\frac{\partial}{\partial x} (3 cos (3 x + 4 y))

\frac{d y}{d t} = \frac{t}{y - 2}, y (- 1) = 0

\frac{d}{d x} (\frac{3}{5 x ^{2}})

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