4.46.13 $x^4{y}^{⁗}(x)+8x^3{y}^{‴}(x)+12x^2{y}^{″}(x)=0$

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

[[_high_order, _missing_y]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0268161 (sec), leaf count = 27

$$\left\{\{y(x)\to \frac{3c_{2}x+c_1}{6x^2}+c_{4}x+c_3\}\right\}$$

Maple ✓
cpu = 0.012 (sec), leaf count = 19

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

DSolve[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] + 3*x*C[2])/(6*x^2) + C[3] + x*C[4]}}

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) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1+_C2/x+_C3*x+_C4/x^2