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

The solution for y^'=(xy^3)/(sqrt(1+x^2)),y(0)=-1 is y=-sqrt(-(2\sqrt{x^2+1)+3)/(4x^2-5)}

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y^'=(xy^3)/(sqrt(1+x^2)),y(0)=-1

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

y = - - \frac{2 x ^{2} + 1 + 3}{4 x ^{2} - 5}

Solution steps

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

Solve separable ODE:

y = - - \frac{2 x ^{2} + 1 + 3}{4 x ^{2} - 5}

y = - - \frac{2 x ^{2} + 1 + 3}{4 x ^{2} - 5}

x \to 4 lim (3 x^{2} - 7 x + 5)

\frac{d}{d x} (- \frac{e ^{\frac{1}{x}}}{x ^{2}})

\int \frac{x}{x + 2} d x

\int 2 cos^{3} (x) d x

\int (2 x - \frac{1}{8 x})^{2} d x

What is the solution for y^'=(xy^3)/(sqrt(1+x^2)),y(0)=-1 ?
The solution for y^'=(xy^3)/(sqrt(1+x^2)),y(0)=-1 is y=-sqrt(-(2\sqrt{x^2+1)+3)/(4x^2-5)}