ODE
\[ \left (x^2-2 x+2\right ) y'''(x)+x^2 \left (-y''(x)\right )+2 x y'(x)-2 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.232981 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {1}{2} \left (c_2 x^2+2 c_1 x+c_3 e^x\right )\right \}\right \}\]
Maple ✓
cpu = 0.142 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} x +x^{2} \textit {\_C2} +\textit {\_C3} \,{\mathrm e}^{x}]\] Mathematica raw input
DSolve[-2*y[x] + 2*x*y'[x] - x^2*y''[x] + (2 - 2*x + x^2)*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*x*C[1] + x^2*C[2] + E^x*C[3])/2}}
Maple raw input
dsolve((x^2-2*x+2)*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))
Maple raw output
[y(x) = _C1*x+x^2*_C2+_C3*exp(x)]