ODE
\[ y(x) y'(x)+y(x)^2+4 x (x+1)=0 \] ODE Classification
[[_homogeneous, `class D`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.0104468 (sec), leaf count = 47
\[\left \{\left \{y(x)\to -\sqrt {c_1 e^{-2 x}-4 x^2}\right \},\left \{y(x)\to \sqrt {c_1 e^{-2 x}-4 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 20
\[ \left \{ 4\,{x}^{2}-{{\rm e}^{-2\,x}}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{2}=0 \right \} \] Mathematica raw input
DSolve[4*x*(1 + x) + y[x]^2 + y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-4*x^2 + C[1]/E^(2*x)]}, {y[x] -> Sqrt[-4*x^2 + C[1]/E^(2*x)]}}
Maple raw input
dsolve(y(x)*diff(y(x),x)+4*(1+x)*x+y(x)^2 = 0, y(x),'implicit')
Maple raw output
4*x^2-exp(-2*x)*_C1+y(x)^2 = 0