4.46.14 $x^4{y}^{⁗}(x)+8x^3{y}^{‴}(x)+ay(x)+12x^2{y}^{″}(x)=0$

ODE
$$x^4{y}^{⁗}(x)+8x^3{y}^{‴}(x)+ay(x)+12x^2{y}^{″}(x)=0$$ ODE Classification

[[_high_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0145875 (sec), leaf count = 116

$$\left\{\{y(x)\to \frac{c_1{x}^{-\frac{1}{2}\sqrt{5-4\sqrt{1-a}}}+c_2{x}^{\frac{1}{2}\sqrt{5-4\sqrt{1-a}}}+c_3{x}^{-\frac{1}{2}\sqrt{4\sqrt{1-a}+5}}+c_4{x}^{\frac{1}{2}\sqrt{4\sqrt{1-a}+5}}}{\sqrt{x}}\}\right\}$$

Maple ✓
cpu = 0.027 (sec), leaf count = 89

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{1}{2}-\frac{1}{2}\sqrt{5-4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{2}{x}^{-\frac{1}{2}+\frac{1}{2}\sqrt{5-4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{3}{x}^{-\frac{1}{2}-\frac{1}{2}\sqrt{5+4\sqrt{1-a}}}+\mathit{\_}\mathit{C}\mathit{4}{x}^{-\frac{1}{2}+\frac{1}{2}\sqrt{5+4\sqrt{1-a}}}\}$$ Mathematica raw input

DSolve[a*y[x] + 12*x^2*y''[x] + 8*x^3*y'''[x] + x^4*y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1]/x^(Sqrt[5 - 4*Sqrt[1 - a]]/2) + x^(Sqrt[5 - 4*Sqrt[1 - a]]/2)*C[
2] + C[3]/x^(Sqrt[5 + 4*Sqrt[1 - a]]/2) + x^(Sqrt[5 + 4*Sqrt[1 - a]]/2)*C[4])/Sq
rt[x]}}

Maple raw input

dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+8*x^3*diff(diff(diff(y(x),x),x),x)+12*x^2*diff(diff(y(x),x),x)+a*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*x^(-1/2-1/2*(5-4*(1-a)^(1/2))^(1/2))+_C2*x^(-1/2+1/2*(5-4*(1-a)^(1/2)
)^(1/2))+_C3*x^(-1/2-1/2*(5+4*(1-a)^(1/2))^(1/2))+_C4*x^(-1/2+1/2*(5+4*(1-a)^(1/
2))^(1/2))