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

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

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

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

Solution steps

\frac{d y}{d 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}

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\frac{d y}{d x} = \frac{2 y}{x} + x^{2} y^{5}

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