4.12.27 $$\left (1-x^2\right ) y(x) y'(x)+2 x^2+x y(x)^2=0$$

ODE
$\left (1-x^2\right ) y(x) y'(x)+2 x^2+x y(x)^2=0$ ODE Classiﬁcation

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.304896 (sec), leaf count = 93

$\left \{\left \{y(x)\to -\sqrt {\left (x^2-1\right ) \log (1-x)-\left (x^2-1\right ) \log (x+1)+c_1 x^2-2 x-c_1}\right \},\left \{y(x)\to \sqrt {\left (x^2-1\right ) \log (1-x)-\left (x^2-1\right ) \log (x+1)+c_1 x^2-2 x-c_1}\right \}\right \}$

Maple
cpu = 0.054 (sec), leaf count = 91

$\left [y \left (x \right ) = \sqrt {\ln \left (x -1\right ) x^{2}-\ln \left (x +1\right ) x^{2}+x^{2} \textit {\_C1} -\ln \left (x -1\right )+\ln \left (x +1\right )-\textit {\_C1} -2 x}, y \left (x \right ) = -\sqrt {\ln \left (x -1\right ) x^{2}-\ln \left (x +1\right ) x^{2}+x^{2} \textit {\_C1} -\ln \left (x -1\right )+\ln \left (x +1\right )-\textit {\_C1} -2 x}\right ]$ Mathematica raw input

DSolve[2*x^2 + x*y[x]^2 + (1 - x^2)*y[x]*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -Sqrt[-2*x - C[1] + x^2*C[1] + (-1 + x^2)*Log[1 - x] - (-1 + x^2)*Log[
1 + x]]}, {y[x] -> Sqrt[-2*x - C[1] + x^2*C[1] + (-1 + x^2)*Log[1 - x] - (-1 + x
^2)*Log[1 + x]]}}

Maple raw input

dsolve((-x^2+1)*y(x)*diff(y(x),x)+2*x^2+x*y(x)^2 = 0, y(x))

Maple raw output

[y(x) = (ln(x-1)*x^2-ln(x+1)*x^2+x^2*_C1-ln(x-1)+ln(x+1)-_C1-2*x)^(1/2), y(x) =
-(ln(x-1)*x^2-ln(x+1)*x^2+x^2*_C1-ln(x-1)+ln(x+1)-_C1-2*x)^(1/2)]