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 = 0.0204605 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {1}{4} x \left (4 c_3 x+4 \left (c_2-3\right ) \log (x)+4 \left (c_1-3\right )+x^2-6 \log ^2(x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -6\, \left ( \ln \left ( x \right ) \right ) ^{2}+ \left ( 4\,{\it \_C3}-12 \right ) \ln \left ( x \right ) +{x}^{2}+4\,{\it \_C2}\,x+4\,{\it \_C1}-12 \right ) x}{4}} \right \} \] 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),'implicit')
Maple raw output
y(x) = 1/4*(-6*ln(x)^2+(4*_C3-12)*ln(x)+x^2+4*_C2*x+4*_C1-12)*x