ODE
\[ x y'(x)=y(x) (2 x y(x)+1) \] ODE Classification
[[_homogeneous, `class D`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.00724698 (sec), leaf count = 18
\[\left \{\left \{y(x)\to -\frac {x}{x^2-c_1}\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 15
\[ \left \{ x-{\frac {{\it \_C1}}{x}}+ \left ( y \left ( x \right ) \right ) ^{-1}=0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == y[x]*(1 + 2*x*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> -(x/(x^2 - C[1]))}}
Maple raw input
dsolve(x*diff(y(x),x) = y(x)*(1+2*x*y(x)), y(x),'implicit')
Maple raw output
x-1/x*_C1+1/y(x) = 0