ODE
\[ \left (-x^2-x+2\right ) y''(x)+(1-x) x y'(x)+x (6 x+7) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.295878 (sec), leaf count = 52
\[\left \{\left \{y(x)\to 39 c_2 e^{2 x-5} (x-1) \text {Ei}(5-5 x)+c_1 \left (-e^{2 x}\right ) (x-1)+\frac {1}{5} c_2 e^{-3 x} (x+44)\right \}\right \}\]
Maple ✓
cpu = 0.109 (sec), leaf count = 43
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{2 x} \left (x -1\right )+\textit {\_C2} \left (-195 \,{\mathrm e}^{2 x -5} \left (x -1\right ) \expIntegral \left (1, 5 x -5\right )+\left (x +44\right ) {\mathrm e}^{-3 x}\right )]\] Mathematica raw input
DSolve[x*(7 + 6*x)*y[x] + (1 - x)*x*y'[x] + (2 - x - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(E^(2*x)*(-1 + x)*C[1]) + ((44 + x)*C[2])/(5*E^(3*x)) + 39*E^(-5 + 2*x)*(-1 + x)*C[2]*ExpIntegralEi[5 - 5*x]}}
Maple raw input
dsolve((-x^2-x+2)*diff(diff(y(x),x),x)+x*(1-x)*diff(y(x),x)+x*(7+6*x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(2*x)*(x-1)+_C2*(-195*exp(2*x-5)*(x-1)*Ei(1,5*x-5)+(x+44)*exp(-3*x))]