ODE
\[ x^2 y''(x)-4 x y'(x)+6 y(x)=x^2 \left (x^2-1\right ) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0142279 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {1}{2} x^2 \left (2 c_2 x+2 c_1+x^2+2 \log (x)+2\right )\right \}\right \}\]
Maple ✓
cpu = 0.031 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2} \left ( 2\,x{\it \_C2}+{x}^{2}+2\,\ln \left ( x \right ) +2\,{\it \_C1}+2 \right ) }{2}} \right \} \] Mathematica raw input
DSolve[6*y[x] - 4*x*y'[x] + x^2*y''[x] == x^2*(-1 + x^2),y[x],x]
Mathematica raw output
{{y[x] -> (x^2*(2 + x^2 + 2*C[1] + 2*x*C[2] + 2*Log[x]))/2}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = x^2*(x^2-1), y(x),'implicit')
Maple raw output
y(x) = 1/2*x^2*(2*x*_C2+x^2+2*ln(x)+2*_C1+2)