ODE
\[ x^2 \left (-y'(x)\right )+y''(x)+x y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.055221 (sec), leaf count = 51
\[\left \{\left \{y(x)\to -c_2 e^{\frac {x^3}{3}}+\frac {c_2 \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},-\frac {x^3}{3}\right )}{\sqrt [3]{3}}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.201 (sec), leaf count = 47
\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{2}} \left ( {{\rm e}^{{\frac {{x}^{3}}{3}}}} \left ( -{x}^{3} \right ) ^{{\frac {2}{3}}}\sqrt [3]{3}{\it \_C2}+{x}^{3} \left ( -\Gamma \left ( {\frac {2}{3}} \right ) {\it \_C2}+{\it \_C2}\,\Gamma \left ( {\frac {2}{3}},-{\frac {{x}^{3}}{3}} \right ) +{\it \_C1} \right ) \right ) } \right \} \] Mathematica raw input
DSolve[x*y[x] - x^2*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] - E^(x^3/3)*C[2] + ((-x^3)^(1/3)*C[2]*Gamma[2/3, -x^3/3])/3^(1/3)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-x^2*diff(y(x),x)+x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (exp(1/3*x^3)*(-x^3)^(2/3)*3^(1/3)*_C2+x^3*(-GAMMA(2/3)*_C2+_C2*GAMMA(2/3,-1/3*x^3)+_C1))/x^2