ODE
\[ x y''(x)-(x+1) y'(x)+y(x)=0 \] ODE Classification
[_Laguerre]
Book solution method
TO DO
Mathematica ✓
cpu = 0.660348 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_1 e^x-c_2 (x+1)\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 13
\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{{\rm e}^{x}}+{\it \_C1}\,x+{\it \_C1} \right \} \] Mathematica raw input
DSolve[y[x] - (1 + x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*C[1] - (1 + x)*C[2]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(1+x)*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C2*exp(x)+_C1*x+_C1