ODE
\[ x^3 y'''(x)+x^2 y''(x)+3 x y'(x)-8 y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.155312 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_3 x^2+c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x))\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 24
\[[y \left (x \right ) = x^{2} \textit {\_C1} +\textit {\_C2} \sin \left (2 \ln \left (x \right )\right )+\textit {\_C3} \cos \left (2 \ln \left (x \right )\right )]\] Mathematica raw input
DSolve[-8*y[x] + 3*x*y'[x] + x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^2*C[3] + C[1]*Cos[2*Log[x]] + C[2]*Sin[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)+3*x*diff(y(x),x)-8*y(x) = 0, y(x))
Maple raw output
[y(x) = x^2*_C1+_C2*sin(2*ln(x))+_C3*cos(2*ln(x))]