ODE
\[ x^3 y'''(x)-x^2 y''(x)+2 x y'(x)-2 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.155379 (sec), leaf count = 19
\[\{\{y(x)\to x (c_3 x+c_2 \log (x)+c_1)\}\}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 18
\[[y \left (x \right ) = x^{2} \textit {\_C1} +\textit {\_C2} x +\textit {\_C3} x \ln \left (x \right )]\] Mathematica raw input
DSolve[-2*y[x] + 2*x*y'[x] - x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1] + x*C[3] + C[2]*Log[x])}}
Maple raw input
dsolve(x^3*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) = x^2*_C1+_C2*x+_C3*x*ln(x)]