4.46.15 $\text{A1}{x}^3{y}^{‴}(x)+x^4{y}^{⁗}(x)+\text{A2}{x}^2{y}^{″}(x)+\text{A3}x{y}^{\prime }(x)+\text{A4}y(x)=0$

ODE
$$\text{A1}{x}^3{y}^{‴}(x)+x^4{y}^{⁗}(x)+\text{A2}{x}^2{y}^{″}(x)+\text{A3}x{y}^{\prime }(x)+\text{A4}y(x)=0$$ ODE Classification

[[_high_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0140151 (sec), leaf count = 186

$$\left\{\{y(x)\to c_1{x}^{\text{Root}[{\mathrm{\#}\text{1}}^4+{\mathrm{\#}\text{1}}^3(\text{A1}-6)+{\mathrm{\#}\text{1}}^2(-3\text{A1}+\text{A2}+11)+\mathrm{\#}\text{1}(2\text{A1}-\text{A2}+\text{A3}-6)+\text{A4}\mathrm{\&},1]}+c_2{x}^{\text{Root}[{\mathrm{\#}\text{1}}^4+{\mathrm{\#}\text{1}}^3(\text{A1}-6)+{\mathrm{\#}\text{1}}^2(-3\text{A1}+\text{A2}+11)+\mathrm{\#}\text{1}(2\text{A1}-\text{A2}+\text{A3}-6)+\text{A4}\mathrm{\&},2]}+c_3{x}^{\text{Root}[{\mathrm{\#}\text{1}}^4+{\mathrm{\#}\text{1}}^3(\text{A1}-6)+{\mathrm{\#}\text{1}}^2(-3\text{A1}+\text{A2}+11)+\mathrm{\#}\text{1}(2\text{A1}-\text{A2}+\text{A3}-6)+\text{A4}\mathrm{\&},3]}+c_4{x}^{\text{Root}[{\mathrm{\#}\text{1}}^4+{\mathrm{\#}\text{1}}^3(\text{A1}-6)+{\mathrm{\#}\text{1}}^2(-3\text{A1}+\text{A2}+11)+\mathrm{\#}\text{1}(2\text{A1}-\text{A2}+\text{A3}-6)+\text{A4}\mathrm{\&},4]}\}\right\}$$

Maple ✓
cpu = 0.018 (sec), leaf count = 51

$$\{y\left(x\right)=\sum _{\mathit{\_}\mathit{a}=1}^4{x}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^4+(\mathit{A}\mathit{1}-6){\mathit{\_}\mathit{Z}}^3+(\mathit{A}\mathit{2}-3\mathit{A}\mathit{1}+11){\mathit{\_}\mathit{Z}}^2+(\mathit{A}\mathit{3}-\mathit{A}\mathit{2}+2\mathit{A}\mathit{1}-6)\mathit{\_}\mathit{Z}+\mathit{A}\mathit{4},\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}=\mathit{\_}\mathit{a})}{\mathit{\_}\mathit{C}}_{\mathit{\_}\mathit{a}}\}$$ Mathematica raw input

DSolve[A4*y[x] + A3*x*y'[x] + A2*x^2*y''[x] + A1*x^3*y'''[x] + x^4*y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x^Root[A4 + (-6 + 2*A1 - A2 + A3)*#1 + (11 - 3*A1 + A2)*#1^2 + (-6 + A
1)*#1^3 + #1^4 & , 1]*C[1] + x^Root[A4 + (-6 + 2*A1 - A2 + A3)*#1 + (11 - 3*A1 +
 A2)*#1^2 + (-6 + A1)*#1^3 + #1^4 & , 2]*C[2] + x^Root[A4 + (-6 + 2*A1 - A2 + A3
)*#1 + (11 - 3*A1 + A2)*#1^2 + (-6 + A1)*#1^3 + #1^4 & , 3]*C[3] + x^Root[A4 + (
-6 + 2*A1 - A2 + A3)*#1 + (11 - 3*A1 + A2)*#1^2 + (-6 + A1)*#1^3 + #1^4 & , 4]*C
[4]}}

Maple raw input

dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+A1*x^3*diff(diff(diff(y(x),x),x),x)+A2*x^2*diff(diff(y(x),x),x)+A3*x*diff(y(x),x)+A4*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = Sum(x^RootOf(_Z^4+(A1-6)*_Z^3+(A2-3*A1+11)*_Z^2+(A3-A2+2*A1-6)*_Z+A4,inde
x = _a)*_C[_a],_a = 1 .. 4)