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 = 0.0431472 (sec), leaf count = 23
\[\left \{\left \{y(x)\to x \left (c_1 x-c_2 \sin (x)+c_3 \cos (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.118 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) =x \left ( \sin \left ( x \right ) {\it \_C3}+\cos \left ( x \right ) {\it \_C2}+{\it \_C1}\,x \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x*(sin(x)*_C3+cos(x)*_C2+_C1*x)