ODE
\[ x^3 y'''(x)+3 x^2 y''(x)-2 x y'(x)+2 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163795 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_1}{x^2}+c_2 x+c_3 x \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x^{2}}+\textit {\_C2} x +\textit {\_C3} x \ln \left (x \right )\right ]\] Mathematica raw input
DSolve[2*y[x] - 2*x*y'[x] + 3*x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/x^2 + x*C[2] + x*C[3]*Log[x]}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*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^2+_C2*x+_C3*x*ln(x)]