4.12.27 $(1-x^2)y(x)y^{\prime }(x)+2x^2+xy(x{)}^2=0$

ODE
$$(1-x^2)y(x)y^{\prime }(x)+2x^2+xy(x{)}^2=0$$ ODE Classification

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica ✓
cpu = 0.0318261 (sec), leaf count = 93

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

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

$$\{{\left(y\left(x\right)\right)}^2-(x^2-1)\ln (-1+x)-\mathit{\_}\mathit{C}\mathit{1}{x}^2+\ln (1+x)x^2+2x+\mathit{\_}\mathit{C}\mathit{1}-\ln (1+x)=0\}$$ 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