ODE
\[ 2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.178316 (sec), leaf count = 33
\[\left \{\left \{y(x)\to (x+1) \log (x+1)+c_1 \sqrt {x+1}+(-2+c_2) x-3+c_2\right \}\right \}\]
Maple ✓
cpu = 0.06 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C2} \left (x +1\right )+\textit {\_C1} \sqrt {x +1}+\ln \left (x +1\right ) x +\ln \left (x +1\right )-2 x -3\right ]\] Mathematica raw input
DSolve[y[x] - (1 + x)*y'[x] + 2*(1 + x)^2*y''[x] == x,y[x],x]
Mathematica raw output
{{y[x] -> -3 + Sqrt[1 + x]*C[1] + x*(-2 + C[2]) + C[2] + (1 + x)*Log[1 + x]}}
Maple raw input
dsolve(2*(x+1)^2*diff(diff(y(x),x),x)-(x+1)*diff(y(x),x)+y(x) = x, y(x))
Maple raw output
[y(x) = _C2*(x+1)+_C1*(x+1)^(1/2)+ln(x+1)*x+ln(x+1)-2*x-3]