##### 4.45.50 $$x^2 y''''(x)=2 y'''(x)$$

ODE
$x^2 y''''(x)=2 y'''(x)$ ODE Classiﬁcation

[[_high_order, _missing_y]]

Book solution method
TO DO

Mathematica
cpu = 0.250857 (sec), leaf count = 60

$\left \{\left \{y(x)\to \frac {1}{6} c_1 \left (2 \left (3 x^2+6 x+2\right ) \text {Ei}\left (-\frac {2}{x}\right )+e^{-2/x} x \left (x^2+5 x+2\right )\right )+c_4 x^2+c_3 x+c_2\right \}\right \}$

Maple
cpu = 0.483 (sec), leaf count = 83

$\left [y \left (x \right ) = \frac {\textit {\_C1} \,x^{3} {\mathrm e}^{-\frac {2}{x}}}{6}+\frac {5 \textit {\_C1} \,{\mathrm e}^{-\frac {2}{x}} x^{2}}{6}-\textit {\_C1} \expIntegral \left (1, \frac {2}{x}\right ) x^{2}+\frac {\textit {\_C1} x \,{\mathrm e}^{-\frac {2}{x}}}{3}-2 \textit {\_C1} \expIntegral \left (1, \frac {2}{x}\right ) x -\frac {2 \textit {\_C1} \expIntegral \left (1, \frac {2}{x}\right )}{3}+\frac {x^{2} \textit {\_C2}}{2}+\textit {\_C3} x +\textit {\_C4}\right ]$ Mathematica raw input

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

Mathematica raw output

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

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))

Maple raw output

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