ODE
\[ y'''(x)+x^2 \left (-y''(x)\right )+2 x y'(x)-2 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.167059 (sec), leaf count = 90
\[\left \{\left \{y(x)\to \frac {1}{12} c_3 \left (3 e^{\frac {x^3}{3}}+\sqrt [3]{3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-\frac {x^3}{3}\right )-2\ 3^{2/3} \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},-\frac {x^3}{3}\right )\right )+\frac {c_2 x^2}{2}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.209 (sec), leaf count = 104
\[ \left \{ y \left ( x \right ) =3\,{\frac { \left ( -3\,\Gamma \left ( 2/3 \right ) {{\rm e}^{1/3\,{x}^{3}}}{\it \_C3}+1/3\,x \left ( {\it \_C2}\,x+{\it \_C1} \right ) \right ) \left ( -{x}^{3} \right ) ^{2/3}+{\it \_C3}\,{x}^{3} \left ( \sqrt [3]{3}\Gamma \left ( 2/3 \right ) \sqrt [3]{-{x}^{3}}\Gamma \left ( 1/3,-1/3\,{x}^{3} \right ) -2/3\,\sqrt [3]{-{x}^{3}}{3}^{5/6}\pi -2\,{3}^{2/3}\Gamma \left ( 2/3 \right ) \Gamma \left ( 2/3,-1/3\,{x}^{3} \right ) +2\,{3}^{2/3} \left ( \Gamma \left ( 2/3 \right ) \right ) ^{2} \right ) }{ \left ( -{x}^{3} \right ) ^{2/3}}} \right \} \] Mathematica raw input
DSolve[-2*y[x] + 2*x*y'[x] - x^2*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + (x^2*C[2])/2 + (C[3]*(3*E^(x^3/3) + 3^(1/3)*(-x^3)^(2/3)*Gamma[1/3, -x^3/3] - 2*3^(2/3)*(-x^3)^(1/3)*Gamma[2/3, -x^3/3]))/12}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = 3*((-3*GAMMA(2/3)*exp(1/3*x^3)*_C3+1/3*x*(_C2*x+_C1))*(-x^3)^(2/3)+_C3*x^3*(3^(1/3)*GAMMA(2/3)*(-x^3)^(1/3)*GAMMA(1/3,-1/3*x^3)-2/3*(-x^3)^(1/3)*3^(5/6)*Pi-2*3^(2/3)*GAMMA(2/3)*GAMMA(2/3,-1/3*x^3)+2*3^(2/3)*GAMMA(2/3)^2))/(-x^3)^(2/3)