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

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

y^{^{'}} = 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

y^{'} (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}

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