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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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

\frac{d y}{d x} + 20 x y = 0

y^{^{'}} = 2 x y - 4 x

y^{^{'}} sec (x) = 8 y^{2}, y (\frac{π}{2}) = \frac{1}{3}

\frac{d P}{d t} = 7 Pt, P (1) = 7

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