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 = 0.0318261 (sec), leaf count = 93

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

Maple
cpu = 0.027 (sec), leaf count = 43

\[ \left \{ \left (y \relax (x ) \right ) ^{2}- \left ({x}^{2}-1 \right ) \ln \left (-1+x \right ) -{\it \_C1}\,{x}^{2}+\ln \left (1+x \right ) {x}^{2}+2\,x+{\it \_C1}-\ln \left (1+x \right ) =0 \right \} \] 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),'implicit')

Maple raw output

y(x)^2-(x^2-1)*ln(-1+x)-_C1*x^2+ln(1+x)*x^2+2*x+_C1-ln(1+x) = 0