ODE
\[ x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2 \] ODE Classification
[[_homogeneous, `class D`], _rational, _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.0119542 (sec), leaf count = 27
\[\left \{\left \{y(x)\to -\frac {x \left (2 c_1+x^2+2\right )}{2 c_1+x^2}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 21
\[ \left \{ -{\frac {x}{x+y \left ( x \right ) }}-{\frac {{x}^{2}}{2}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x*y'[x] == x^3 + (1 + 2*x^2)*y[x] + x*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -((x*(2 + x^2 + 2*C[1]))/(x^2 + 2*C[1]))}}
Maple raw input
dsolve(x*diff(y(x),x) = x^3+(2*x^2+1)*y(x)+x*y(x)^2, y(x),'implicit')
Maple raw output
-x/(x+y(x))-1/2*x^2-_C1 = 0