ODE
\[ x y''(x)-(x+3) y'(x)+3 y(x)=0 \] ODE Classification
[_Laguerre]
Book solution method
TO DO
Mathematica ✓
cpu = 0.172524 (sec), leaf count = 29
\[\left \{\left \{y(x)\to c_1 e^x-c_2 \left (x^3+3 x^2+6 x+6\right )\right \}\right \}\]
Maple ✓
cpu = 0.058 (sec), leaf count = 24
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \left (x^{3}+3 x^{2}+6 x +6\right )]\] Mathematica raw input
DSolve[3*y[x] - (3 + x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*C[1] - (6 + 6*x + 3*x^2 + x^3)*C[2]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(3+x)*diff(y(x),x)+3*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(x)+_C2*(x^3+3*x^2+6*x+6)]