4.9.26 \(y(x) y'(x)+y(x)^2+4 x (x+1)=0\)

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

\[ \left \{ 4\,{x}^{2}-{{\rm e}^{-2\,x}}{\it \_C1}+ \left (y \relax (x ) \right ) ^{2}=0 \right \} \] 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