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 = 0.013271 (sec), leaf count = 30

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

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

\[ \left \{ y \relax (x ) =-{\frac { \left ({\it \_C1}\,{{\sl Y}_{1}\relax (x)}+{{\sl J}_{1}\relax (x)} \right ) x}{{\it \_C1}\,{{\sl Y}_{0}\relax (x)}+{{\sl J}_{0}\relax (x)}}} \right \} \] 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))