ODE
\[ x y''(x)-(x+3) y'(x)+y(x)=0 \] ODE Classification
[_Laguerre]
Book solution method
TO DO
Mathematica ✓
cpu = 0.206138 (sec), leaf count = 26
\[\left \{\left \{y(x)\to c_2 e^x \left (x^2-4 x+6\right )+c_1 (x+3)\right \}\right \}\]
Maple ✓
cpu = 0.062 (sec), leaf count = 22
\[[y \left (x \right ) = \textit {\_C1} \left (3+x \right )+\textit {\_C2} \,{\mathrm e}^{x} \left (x^{2}-4 x +6\right )]\] Mathematica raw input
DSolve[y[x] - (3 + x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3 + x)*C[1] + E^x*(6 - 4*x + x^2)*C[2]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(3+x)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(3+x)+_C2*exp(x)*(x^2-4*x+6)]