ODE
\[ x y'(x)=y(x) (x y(x)+1) \] ODE Classification
[[_homogeneous, `class D`], _rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.00687323 (sec), leaf count = 18
\[\left \{\left \{y(x)\to -\frac {2 x}{x^2-2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 17
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{-1}+{\frac {x}{2}}-{\frac {{\it \_C1}}{x}}=0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == y[x]*(1 + x*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> (-2*x)/(x^2 - 2*C[1])}}
Maple raw input
dsolve(x*diff(y(x),x) = (1+x*y(x))*y(x), y(x),'implicit')
Maple raw output
1/y(x)+1/2*x-1/x*_C1 = 0