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 = 0.0131348 (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 = 0.037 (sec), leaf count = 14
\[ \left \{ y \left ( x \right ) ={{\rm e}^{x}} \left ( {\it \_C2}\,{x}^{2}+{\it \_C1} \right ) \right \} \] 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)+(1+x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(x)*(_C2*x^2+_C1)