x3y′′′′(x) + 2x2y′′′(x) + a4( −x3) y(x) −xy′′(x) = 0

4.46.8 $x^{3} y^{⁗} (x) + 2 x^{2} y^{‴} (x) + a^{4} (- x^{3}) y (x) - x y^{″} (x) = 0$

ODE
$x^{3} y^{⁗} (x) + 2 x^{2} y^{‴} (x) + a^{4} (- x^{3}) y (x) - x y^{″} (x) = 0$ ODE Classiﬁcation

[[_high_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.839093 (sec), leaf count = 310

${{y (x) \to c_{1}_{0} F_{3} (; \frac{3}{4}, \frac{5}{8} - \frac{\sqrt{5}}{8}, \frac{5}{8} + \frac{\sqrt{5}}{8}; \frac{a^{4} x^{4}}{256}) + 2^{- 3 - \sqrt{5}} ((- 1)^{\frac{1}{8} (3 - \sqrt{5})} a^{\frac{3}{2} - \frac{\sqrt{5}}{2}} x^{\frac{3}{2} - \frac{\sqrt{5}}{2}} (4^{\sqrt{5}} c_{3}_{0} F_{3} (; 1 - \frac{\sqrt{5}}{4}, \frac{9}{8} - \frac{\sqrt{5}}{8}, \frac{11}{8} - \frac{\sqrt{5}}{8}; \frac{a^{4} x^{4}}{256}) + (- 1)^{\frac{\sqrt{5}}{4}} a^{\sqrt{5}} c_{4} x^{\sqrt{5}}_{0} F_{3} (; \frac{9}{8} + \frac{\sqrt{5}}{8}, \frac{11}{8} + \frac{\sqrt{5}}{8}, 1 + \frac{\sqrt{5}}{4}; \frac{a^{4} x^{4}}{256})) + (1 + i) 2^{\frac{1}{2} + \sqrt{5}} a c_{2} x_{0} F_{3} (; \frac{5}{4}, \frac{7}{8} - \frac{\sqrt{5}}{8}, \frac{7}{8} + \frac{\sqrt{5}}{8}; \frac{a^{4} x^{4}}{256}))}}$

Maple ✓
cpu = 0.215 (sec), leaf count = 148

${y (x) =_C 1_{0} F_{3} (; \frac{3}{4}, \frac{5}{8} + \frac{\sqrt{5}}{8}, \frac{5}{8} - \frac{\sqrt{5}}{8}; \frac{a^{4} x^{4}}{256}) +_C 2 x_{0} F_{3} (; \frac{5}{4}, \frac{7}{8} + \frac{\sqrt{5}}{8}, \frac{7}{8} - \frac{\sqrt{5}}{8}; \frac{a^{4} x^{4}}{256}) +_C 3 x^{\frac{3}{2} - \frac{\sqrt{5}}{2}}_{0} F_{3} (; 1 - \frac{\sqrt{5}}{4}, \frac{9}{8} - \frac{\sqrt{5}}{8}, \frac{11}{8} - \frac{\sqrt{5}}{8}; \frac{a^{4} x^{4}}{256}) +_C 4 x^{\frac{3}{2} + \frac{\sqrt{5}}{2}}_{0} F_{3} (; 1 + \frac{\sqrt{5}}{4}, \frac{9}{8} + \frac{\sqrt{5}}{8}, \frac{11}{8} + \frac{\sqrt{5}}{8}; \frac{a^{4} x^{4}}{256})}$ Mathematica raw input

DSolve[-(a^4*x^3*y[x]) - x*y''[x] + 2*x^2*y'''[x] + x^3*y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]*HypergeometricPFQ[{}, {3/4, 5/8 - Sqrt[5]/8, 5/8 + Sqrt[5]/8}, (a
^4*x^4)/256] + 2^(-3 - Sqrt[5])*((1 + I)*2^(1/2 + Sqrt[5])*a*x*C[2]*Hypergeometr
icPFQ[{}, {5/4, 7/8 - Sqrt[5]/8, 7/8 + Sqrt[5]/8}, (a^4*x^4)/256] + (-1)^((3 - S
qrt[5])/8)*a^(3/2 - Sqrt[5]/2)*x^(3/2 - Sqrt[5]/2)*(4^Sqrt[5]*C[3]*Hypergeometri
cPFQ[{}, {1 - Sqrt[5]/4, 9/8 - Sqrt[5]/8, 11/8 - Sqrt[5]/8}, (a^4*x^4)/256] + (-
1)^(Sqrt[5]/4)*a^Sqrt[5]*x^Sqrt[5]*C[4]*HypergeometricPFQ[{}, {9/8 + Sqrt[5]/8,
11/8 + Sqrt[5]/8, 1 + Sqrt[5]/4}, (a^4*x^4)/256]))}}

Maple raw input

dsolve(x^3*diff(diff(diff(diff(y(x),x),x),x),x)+2*x^2*diff(diff(diff(y(x),x),x),x)-x*diff(diff(y(x),x),x)-a^4*x^3*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*hypergeom([],[3/4, 5/8+1/8*5^(1/2), 5/8-1/8*5^(1/2)],1/256*a^4*x^4)+_
C2*x*hypergeom([],[5/4, 7/8+1/8*5^(1/2), 7/8-1/8*5^(1/2)],1/256*a^4*x^4)+_C3*x^(
3/2-1/2*5^(1/2))*hypergeom([],[1-1/4*5^(1/2), 9/8-1/8*5^(1/2), 11/8-1/8*5^(1/2)]
,1/256*a^4*x^4)+_C4*x^(3/2+1/2*5^(1/2))*hypergeom([],[1+1/4*5^(1/2), 9/8+1/8*5^(
1/2), 11/8+1/8*5^(1/2)],1/256*a^4*x^4)

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4.46.8 x3y⁗(x)+2x2y‴(x)+a4(−x3)y(x)−xy″(x)=0

4.46.8 $x^{3} y^{⁗} (x) + 2 x^{2} y^{‴} (x) + a^{4} (- x^{3}) y (x) - x y^{″} (x) = 0$