ODE
\[ x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.1671 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {1}{2} e^x \left (c_2 x^2+2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.064 (sec), leaf count = 16
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,x^{2} {\mathrm e}^{x}]\] Mathematica raw input
DSolve[(1 + x)*y[x] - (1 + 2*x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^x*(2*C[1] + x^2*C[2]))/2}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(1+2*x)*diff(y(x),x)+(x+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(x)+_C2*x^2*exp(x)]