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 = 0.160951 (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 = 0.017 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x^{4}}+x^{2} \textit {\_C2} +\textit {\_C3} x\right ]\] 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))
Maple raw output
[y(x) = 1/x^4*_C1+x^2*_C2+_C3*x]