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 = 0.250621 (sec), leaf count = 47
\[\left \{\left \{y(x)\to -\sqrt {-4 x^2+c_1 e^{-2 x}}\right \},\left \{y(x)\to \sqrt {-4 x^2+c_1 e^{-2 x}}\right \}\right \}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 37
\[\left [y \left (x \right ) = \sqrt {{\mathrm e}^{-2 x} \textit {\_C1} -4 x^{2}}, y \left (x \right ) = -\sqrt {{\mathrm e}^{-2 x} \textit {\_C1} -4 x^{2}}\right ]\] 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))
Maple raw output
[y(x) = (exp(-2*x)*_C1-4*x^2)^(1/2), y(x) = -(exp(-2*x)*_C1-4*x^2)^(1/2)]