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 = 0.0107701 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_3 x^2+c_2 \sin (2 \log (x))+c_1 \cos (2 \log (x))\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}+{\it \_C2}\,\sin \left ( 2\,\ln \left ( x \right ) \right ) +{\it \_C3}\,\cos \left ( 2\,\ln \left ( x \right ) \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*x^2+_C2*sin(2*ln(x))+_C3*cos(2*ln(x))