ODE
\[ x \left (x^2-2 x+2\right ) y'''(x)+\left (-x^3+3 x^2-6 x+6\right ) y''(x)=0 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.230626 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {c_1 e^x}{x}+c_3 x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.162 (sec), leaf count = 16
\[\left [y \left (x \right ) = \frac {{\mathrm e}^{x} \textit {\_C1}}{x}+\textit {\_C2} x +\textit {\_C3}\right ]\] Mathematica raw input
DSolve[(6 - 6*x + 3*x^2 - x^3)*y''[x] + x*(2 - 2*x + x^2)*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^x*C[1])/x + C[2] + x*C[3]}}
Maple raw input
dsolve(x*(x^2-2*x+2)*diff(diff(diff(y(x),x),x),x)+(-x^3+3*x^2-6*x+6)*diff(diff(y(x),x),x) = 0, y(x))
Maple raw output
[y(x) = exp(x)*_C1/x+_C2*x+_C3]