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 = 0.345328 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -\sqrt {x^2+c_1 e^{\frac {1}{x}}}\right \},\left \{y(x)\to \sqrt {x^2+c_1 e^{\frac {1}{x}}}\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 33
\[\left [y \left (x \right ) = \sqrt {{\mathrm e}^{\frac {1}{x}} \textit {\_C1} +x^{2}}, y \left (x \right ) = -\sqrt {{\mathrm e}^{\frac {1}{x}} \textit {\_C1} +x^{2}}\right ]\] 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))
Maple raw output
[y(x) = (exp(1/x)*_C1+x^2)^(1/2), y(x) = -(exp(1/x)*_C1+x^2)^(1/2)]