ODE
\[ 2 x y(x) y'(x)=4 (2 x+1) x^2+y(x)^2 \] ODE Classification
[_rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.00829588 (sec), leaf count = 52
\[\left \{\left \{y(x)\to -\sqrt {x} \sqrt {c_1+4 x^2+4 x}\right \},\left \{y(x)\to \sqrt {x} \sqrt {c_1+4 x^2+4 x}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 22
\[ \left \{ -4\,{x}^{3}+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}\,x-4\,{x}^{2}=0 \right \} \] Mathematica raw input
DSolve[2*x*y[x]*y'[x] == 4*x^2*(1 + 2*x) + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[x]*Sqrt[4*x + 4*x^2 + C[1]])}, {y[x] -> Sqrt[x]*Sqrt[4*x + 4*x^2 + C[1]]}}
Maple raw input
dsolve(2*x*y(x)*diff(y(x),x) = 4*x^2*(1+2*x)+y(x)^2, y(x),'implicit')
Maple raw output
-4*x^3+y(x)^2-_C1*x-4*x^2 = 0