ODE
\[ x y'(x)=x^2+y(x) (y(x)+1) \] ODE Classification
[[_homogeneous, `class D`], _rational, _Riccati]
Book solution method
Riccati ODE, Special cases
Mathematica ✓
cpu = 0.010818 (sec), leaf count = 12
\[\left \{\left \{y(x)\to x \tan \left (c_1+x\right )\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 17
\[ \left \{ \arctan \left ( {\frac {y \left ( x \right ) }{x}} \right ) -x-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == x^2 + y[x]*(1 + y[x]),y[x],x]
Mathematica raw output
{{y[x] -> x*Tan[x + C[1]]}}
Maple raw input
dsolve(x*diff(y(x),x) = x^2+y(x)*(1+y(x)), y(x),'implicit')
Maple raw output
arctan(y(x)/x)-x-_C1 = 0