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 = 0.17113 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \frac {1}{2} x^2 \left (x^2+2 \log (x)+2 c_2 x+2+2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.089 (sec), leaf count = 29
\[\left [y \left (x \right ) = x^{2} \textit {\_C2} +\textit {\_C1} \,x^{3}+\frac {x^{2} \left (x^{2}+2 \ln \left (x \right )+2\right )}{2}\right ]\] 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))
Maple raw output
[y(x) = x^2*_C2+_C1*x^3+1/2*x^2*(x^2+2*ln(x)+2)]