4.4.33 \(a x^2 y(x)^2+x y'(x)+2 y(x)=b\)

ODE
\[ a x^2 y(x)^2+x y'(x)+2 y(x)=b \] ODE Classification

[_rational, _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.0478848 (sec), leaf count = 101

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

Maple
cpu = 0.111 (sec), leaf count = 66

\[ \left \{ y \relax (x ) =-{\frac {1}{ax}\sqrt {-ab} \left ({{\sl Y}_{1}\left (\sqrt {-ab}x\right )}{\it \_C1}+{{\sl J}_{1}\left (\sqrt {-ab}x\right )} \right ) \left ({\it \_C1}\,{{\sl Y}_{0}\left (\sqrt {-ab}x\right )}+{{\sl J}_{0}\left (\sqrt {-ab}x\right )} \right ) ^{-1}} \right \} \] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

dsolve(x*diff(y(x),x)+a*x^2*y(x)^2+2*y(x) = b, y(x),'implicit')

Maple raw output

y(x) = -(-a*b)^(1/2)*(BesselY(1,(-a*b)^(1/2)*x)*_C1+BesselJ(1,(-a*b)^(1/2)*x))/a
/x/(_C1*BesselY(0,(-a*b)^(1/2)*x)+BesselJ(0,(-a*b)^(1/2)*x))