ODE
\[ x^3 y'''(x)-4 x^2 y''(x)+\left (x^2+8\right ) x y'(x)-2 \left (x^2+4\right ) y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.191927 (sec), leaf count = 23
\[\{\{y(x)\to x (c_1 x+c_3 \cos (x)-c_2 \sin (x))\}\}\]
Maple ✓
cpu = 0.193 (sec), leaf count = 20
\[[y \left (x \right ) = x^{2} \textit {\_C1} +\textit {\_C2} x \cos \left (x \right )+\textit {\_C3} x \sin \left (x \right )]\] Mathematica raw input
DSolve[-2*(4 + x^2)*y[x] + x*(8 + x^2)*y'[x] - 4*x^2*y''[x] + x^3*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(x*C[1] + C[3]*Cos[x] - C[2]*Sin[x])}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)-4*x^2*diff(diff(y(x),x),x)+x*(x^2+8)*diff(y(x),x)-2*(x^2+4)*y(x) = 0, y(x))
Maple raw output
[y(x) = x^2*_C1+_C2*x*cos(x)+_C3*x*sin(x)]