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 = 0.0856123 (sec), leaf count = 60
\[\left \{\left \{y(x)\to \frac {1}{5} e^{-3 x-5} \left (195 c_2 e^{5 x} (x-1) \text {Ei}(5-5 x)-e^5 \left (5 c_1 e^{5 x} (x-1)-c_2 (x+44)\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.085 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) =-195\,{{\rm e}^{2\,x-5}}{\it \_C2}\, \left ( -1+x \right ) {\it Ei} \left ( 1,5\,x-5 \right ) +{\it \_C2}\, \left ( x+44 \right ) {{\rm e}^{-3\,x}}+{\it \_C1}\,{{\rm e}^{2\,x}} \left ( -1+x \right ) \right \} \] 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^(-5 - 3*x)*(-(E^5*(5*E^(5*x)*(-1 + x)*C[1] - (44 + x)*C[2])) + 195*E^(5*x)*(-1 + x)*C[2]*ExpIntegralEi[5 - 5*x]))/5}}
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),'implicit')
Maple raw output
y(x) = -195*exp(2*x-5)*_C2*(-1+x)*Ei(1,5*x-5)+_C2*(x+44)*exp(-3*x)+_C1*exp(2*x)*(-1+x)