4.4.16 $x^2+x{y}^{\prime }(x)+y(x{)}^2=0$

ODE
$$x^2+x{y}^{\prime }(x)+y(x{)}^2=0$$ ODE Classification

[_rational, _Riccati]

Book solution method
Riccati ODE, Special cases

Mathematica ✓
cpu = 0.013271 (sec), leaf count = 30

$$\left\{\{y(x)\to -\frac{x(c_1{J}_1(x)+Y_1(x))}{c_1{J}_0(x)+Y_0(x)}\}\right\}$$

Maple ✓
cpu = 0.087 (sec), leaf count = 27

$$\{y\left(x\right)=-\frac{(\mathit{\_}\mathit{C}\mathit{1}{\mathit{Y}}_1\left(x\right)+{\mathit{J}}_1\left(x\right))x}{\mathit{\_}\mathit{C}\mathit{1}{\mathit{Y}}_0\left(x\right)+{\mathit{J}}_0\left(x\right)}\}$$ 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),'implicit')

Maple raw output

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