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 = 0.161676 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_1}{x^3}+c_2 x^2+\frac {x}{4}-\frac {1}{3}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 19
\[\left [y \left (x \right ) = x^{2} \textit {\_C2} +\frac {\textit {\_C1}}{x^{3}}+\frac {x}{4}-\frac {1}{3}\right ]\] 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 + C[1]/x^3 + x^2*C[2]}}
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))
Maple raw output
[y(x) = x^2*_C2+1/x^3*_C1+1/4*x-1/3]