ODE
\[ x^3 y'''(x)+2 x^2 y''(x)-x y'(x)+y(x)=0 \] ODE Classification
[[_3rd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0101637 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_1}{x}+c_2 x+c_3 x \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C3}\,{x}^{2}\ln \left ( x \right ) +{\it \_C2}\,{x}^{2}+{\it \_C1}}{x}} \right \} \] Mathematica raw input
DSolve[y[x] - x*y'[x] + 2*x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/x + x*C[2] + x*C[3]*Log[x]}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C3*x^2*ln(x)+_C2*x^2+_C1)/x