##### 4.4.16 $$x^2+x y'(x)+y(x)^2=0$$

ODE
$x^2+x y'(x)+y(x)^2=0$ ODE Classiﬁcation

[_rational, _Riccati]

Book solution method
Riccati ODE, Special cases

Mathematica
cpu = 0.239035 (sec), leaf count = 30

$\left \{\left \{y(x)\to -\frac {x (Y_1(x)+c_1 J_1(x))}{Y_0(x)+c_1 J_0(x)}\right \}\right \}$

Maple
cpu = 0.085 (sec), leaf count = 40

$\left [y \left (x \right ) = -\frac {x \textit {\_C1} \BesselY \left (1, x\right )}{\textit {\_C1} \BesselY \left (0, x\right )+\BesselJ \left (0, x\right )}-\frac {\BesselJ \left (1, x\right ) x}{\textit {\_C1} \BesselY \left (0, x\right )+\BesselJ \left (0, x\right )}\right ]$ Mathematica raw input

DSolve[x^2 + y[x]^2 + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((x*(BesselY[1, x] + BesselJ[1, x]*C[1]))/(BesselY[0, x] + BesselJ[0,
 x]*C[1]))}}

Maple raw input

dsolve(x*diff(y(x),x)+x^2+y(x)^2 = 0, y(x))

Maple raw output

[y(x) = -x*_C1/(_C1*BesselY(0,x)+BesselJ(0,x))*BesselY(1,x)-BesselJ(1,x)*x/(_C1*
BesselY(0,x)+BesselJ(0,x))]