ODE
\[ x^3 y'''(x)+4 x^2 y''(x)-8 x y'(x)+8 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0108917 (sec), leaf count = 22
\[\left \{\left \{y(x)\to \frac {c_1}{x^4}+c_3 x^2+c_2 x\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,{x}^{6}+{\it \_C1}\,{x}^{5}+{\it \_C3}}{{x}^{4}}} \right \} \] Mathematica raw input
DSolve[8*y[x] - 8*x*y'[x] + 4*x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/x^4 + x*C[2] + x^2*C[3]}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+4*x^2*diff(diff(y(x),x),x)-8*x*diff(y(x),x)+8*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*x^6+_C1*x^5+_C3)/x^4