ODE
\[ x^3 y'''(x)-x^2 y''(x)+2 x y'(x)-2 y(x)=x \left (x^2+3\right ) \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.162128 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {1}{4} x \left (x^2-6 \log ^2(x)+4 c_3 x+4 (-3+c_2) \log (x)+4 (-3+c_1)\right )\right \}\right \}\]
Maple ✓
cpu = 0.065 (sec), leaf count = 38
\[\left [y \left (x \right ) = -\frac {x \left (6 \ln \left (x \right )^{2}-x^{2}+12 \ln \left (x \right )+12\right )}{4}+\textit {\_C1} x +x^{2} \textit {\_C2} +\textit {\_C3} x \ln \left (x \right )\right ]\] Mathematica raw input
DSolve[-2*y[x] + 2*x*y'[x] - x^2*y''[x] + x^3*y'''[x] == x*(3 + x^2),y[x],x]
Mathematica raw output
{{y[x] -> (x*(x^2 + 4*(-3 + C[1]) + 4*x*C[3] + 4*(-3 + C[2])*Log[x] - 6*Log[x]^2))/4}}
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)-x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-2*y(x) = x*(x^2+3), y(x))
Maple raw output
[y(x) = -1/4*x*(6*ln(x)^2-x^2+12*ln(x)+12)+_C1*x+x^2*_C2+_C3*x*ln(x)]