ODE
\[ 2 x^2 y(x) y'(x)=x^2 (2 x+1)-y(x)^2 \] ODE Classification
[[_homogeneous, `class D`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.0110721 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -\sqrt {c_1 e^{\frac {1}{x}}+x^2}\right \},\left \{y(x)\to \sqrt {c_1 e^{\frac {1}{x}}+x^2}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 20
\[ \left \{ -{x}^{2}-{{\rm e}^{{x}^{-1}}}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{2}=0 \right \} \] Mathematica raw input
DSolve[2*x^2*y[x]*y'[x] == x^2*(1 + 2*x) - y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[x^2 + E^x^(-1)*C[1]]}, {y[x] -> Sqrt[x^2 + E^x^(-1)*C[1]]}}
Maple raw input
dsolve(2*x^2*y(x)*diff(y(x),x) = x^2*(1+2*x)-y(x)^2, y(x),'implicit')
Maple raw output
-x^2-exp(1/x)*_C1+y(x)^2 = 0