ODE
\[ x^2 y''(x)+2 x y'(x)-6 y(x)=2-x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0191627 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_2}{x^3}+c_1 x^2+\frac {x}{4}-\frac {1}{3}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}}{{x}^{3}}}+{x}^{2}{\it \_C1}+{\frac {x}{4}}-{\frac {1}{3}} \right \} \] Mathematica raw input
DSolve[-6*y[x] + 2*x*y'[x] + x^2*y''[x] == 2 - x,y[x],x]
Mathematica raw output
{{y[x] -> -1/3 + x/4 + x^2*C[1] + C[2]/x^3}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-6*y(x) = 2-x, y(x),'implicit')
Maple raw output
y(x) = 1/x^3*_C2+x^2*_C1+1/4*x-1/3