ODE
\[ x^2 y''(x)+(2-x) x y'(x)-(3 x+2) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0208458 (sec), leaf count = 41
\[\left \{\left \{y(x)\to c_1 e^x x-\frac {c_2 \left (e^x x^3 \text {Ei}(-x)+x^2-x+2\right )}{6 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.048 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{x}}{\it Ei} \left ( 1,x \right ) {\it \_C2}\,{x}^{3}+{\it \_C1}\,{x}^{3}{{\rm e}^{x}}-{\it \_C2}\, \left ( {x}^{2}-x+2 \right ) }{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[-((2 + 3*x)*y[x]) + (2 - x)*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*x*C[1] - (C[2]*(2 - x + x^2 + E^x*x^3*ExpIntegralEi[-x]))/(6*x^2)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*(2-x)*diff(y(x),x)-(2+3*x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (exp(x)*Ei(1,x)*_C2*x^3+_C1*x^3*exp(x)-_C2*(x^2-x+2))/x^2