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 = 0.245564 (sec), leaf count = 12
\[\{\{y(x)\to x \tan (x+c_1)\}\}\]
Maple ✓
cpu = 0.03 (sec), leaf count = 10
\[[y \left (x \right ) = \tan \left (x +\textit {\_C1} \right ) x]\] 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))
Maple raw output
[y(x) = tan(x+_C1)*x]