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 = 0.190796 (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 = 0.085 (sec), leaf count = 32
\[\left [y \left (x \right ) = {\mathrm e}^{x} \textit {\_C1} x +\frac {\textit {\_C2} \left (x^{3} {\mathrm e}^{x} \expIntegral \left (1, x\right )-x^{2}+x -2\right )}{x^{2}}\right ]\] 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))
Maple raw output
[y(x) = exp(x)*_C1*x+_C2*(x^3*exp(x)*Ei(1,x)-x^2+x-2)/x^2]