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 = 0.0314527 (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 = 0.085 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) =x \left ( -\Gamma \left ( {\frac {2}{3}} \right ) \Gamma \left ( {\frac {1}{3}},-{\frac {1}{3\,{x}^{3}}} \right ) \sqrt {3}{\it \_C2}+2\,\pi \,{\it \_C2}+{\it \_C1} \right ) \right \} \] 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*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),'implicit')
Maple raw output
y(x) = x*(-GAMMA(2/3)*GAMMA(1/3,-1/3/x^3)*3^(1/2)*_C2+2*Pi*_C2+_C1)