4.1489   axy ′(x)+ y(x)(b+ cx3)+ x2y′′(x ) = 0

ODE

axy′(x)+ y(x)(b+ cx3)+ x2y′′(x) = 0

ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0802224 (sec), leaf count = 156

{{                    (    (     ∘ --------------)              (        )      (  ∘ --------------  )              (        ))} }
   y(x) → 3a−31c16− a6 x12− a2 c1Γ 1 − 1 a2 − 2a − 4b+ 1 J 1√-2-------  2√cx3∕2  + c2Γ  1   a2 − 2a− 4b+ 1 +1 J1√ 2-------- 2 √cx3∕2
                                3                  − 3 a −2a−4b+1  3              3                      3  a−2a−4b+1  3

Maple
cpu = 0.039 (sec), leaf count = 65

{             (              (      )                   (      )    )}
  y(x) = x− a2+12 Y1√-2-------  2√cx 32  C2 + J1√-2-------  2 √cx32  C1
                 3 a −2a−4b+1  3             3 a −2a−4b+1  3

Mathematica raw input

DSolve[(b + c*x^3)*y[x] + a*x*y'[x] + x^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> 3^((-1 + a)/3)*c^(1/6 - a/6)*x^(1/2 - a/2)*(BesselJ[-Sqrt[1 - 2*a + a^
2 - 4*b]/3, (2*Sqrt[c]*x^(3/2))/3]*C[1]*Gamma[1 - Sqrt[1 - 2*a + a^2 - 4*b]/3] +
 BesselJ[Sqrt[1 - 2*a + a^2 - 4*b]/3, (2*Sqrt[c]*x^(3/2))/3]*C[2]*Gamma[1 + Sqrt
[1 - 2*a + a^2 - 4*b]/3])}}

Maple raw input

dsolve(x^2*diff(diff(y(x),x),x)+a*x*diff(y(x),x)+(c*x^3+b)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x^(-1/2*a+1/2)*(BesselY(1/3*(a^2-2*a-4*b+1)^(1/2),2/3*c^(1/2)*x^(3/2))*_C
2+BesselJ(1/3*(a^2-2*a-4*b+1)^(1/2),2/3*c^(1/2)*x^(3/2))*_C1)