ODE
\[ -\left (-x^2-x+1\right ) y(x)+y''(x)-(2 x+1) y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0138564 (sec), leaf count = 24
\[\left \{\left \{y(x)\to e^{\frac {x^2}{2}} \left (c_2 e^x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.05 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}}+{\it \_C2}\,{{\rm e}^{{\frac {x \left ( 2+x \right ) }{2}}}} \right \} \] Mathematica raw input
DSolve[-((1 - x - x^2)*y[x]) - (1 + 2*x)*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(x^2/2)*(C[1] + E^x*C[2])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-(1+2*x)*diff(y(x),x)-(-x^2-x+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*exp(1/2*x^2)+_C2*exp(1/2*x*(2+x))