4.45.50 $x^2{y}^{⁗}(x)=2y^{‴}(x)$

ODE
$$x^2{y}^{⁗}(x)=2y^{‴}(x)$$ ODE Classification

[[_high_order, _missing_y]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0609586 (sec), leaf count = 62

$$\left\{\{y(x)\to \frac{1}{3}{c}_1(3x^2+6x+2)\text{Ei}(-\frac{2}{x})+c_4{x}^2+\frac{1}{6}{c}_1{e}^{-2/x}(x^2+5x+2)x+c_{3}x+c_2\}\right\}$$

Maple ✓
cpu = 0.138 (sec), leaf count = 51

$$\{y\left(x\right)=-\mathit{\_}\mathit{C}\mathit{1}(x^2+2x+\frac{2}{3})\mathit{E}\mathit{i}(1,2x^{-1})+\frac{x\mathit{\_}\mathit{C}\mathit{1}(x^2+5x+2)}{6}{\mathrm{e}}^{-2x^{-1}}+\frac{\mathit{\_}\mathit{C}\mathit{2}{x}^2}{2}+\mathit{\_}\mathit{C}\mathit{3}x+\mathit{\_}\mathit{C}\mathit{4}\}$$ Mathematica raw input

DSolve[x^2*y''''[x] == 2*y'''[x],y[x],x]

Mathematica raw output

{{y[x] -> (x*(2 + 5*x + x^2)*C[1])/(6*E^(2/x)) + C[2] + x*C[3] + x^2*C[4] + ((2 
+ 6*x + 3*x^2)*C[1]*ExpIntegralEi[-2/x])/3}}

Maple raw input

dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x) = 2*diff(diff(diff(y(x),x),x),x), y(x),'implicit')

Maple raw output

y(x) = -_C1*(x^2+2*x+2/3)*Ei(1,2/x)+1/6*x*_C1*(x^2+5*x+2)*exp(-2/x)+1/2*_C2*x^2+
_C3*x+_C4