ODE
\[ x^5 y''(x)+x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.256579 (sec), leaf count = 38
\[\left \{\left \{y(x)\to \frac {c_2 \Gamma \left (\frac {1}{3},-\frac {1}{3 x^3}\right )}{3^{2/3} \sqrt [3]{-\frac {1}{x^3}}}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.41 (sec), leaf count = 29
\[\left [y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} x \left (2 \sqrt {3}\, \pi -3 \Gamma \left (\frac {1}{3}, -\frac {1}{3 x^{3}}\right ) \Gamma \left (\frac {2}{3}\right )\right )\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + x^5*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + (C[2]*Gamma[1/3, -1/3*1/x^3])/(3^(2/3)*(-x^(-3))^(1/3))}}
Maple raw input
dsolve(x^5*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x+_C2*x*(2*3^(1/2)*Pi-3*GAMMA(1/3,-1/3/x^3)*GAMMA(2/3))]