4.4.17 \(x y'(x)=x^2+y(x) (y(x)+1)\)

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

\[ \left \{ \arctan \left ({\frac {y \relax (x ) }{x}} \right ) -x-{\it \_C1}=0 \right \} \] 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