ODE
\[ 2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0410238 (sec), leaf count = 22
\[\left \{\left \{y(x)\to c_1 \sqrt {x+1}+c_2 (x+1)\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {1+x}+{\it \_C2}\,x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[y[x] - (1 + x)*y'[x] + 2*(1 + x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[1 + x]*C[1] + (1 + x)*C[2]}}
Maple raw input
dsolve(2*(1+x)^2*diff(diff(y(x),x),x)-(1+x)*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*(1+x)^(1/2)+_C2*x+_C2