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 = 0.0344311 (sec), leaf count = 33
\[\left \{\left \{y(x)\to c_1 \sqrt {x+1}+\left (c_2-2\right ) x+c_2+(x+1) \log (x+1)-3\right \}\right \}\]
Maple ✓
cpu = 0.029 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) =\sqrt {1+x}{\it \_C2}+ \left ( 1+x \right ) \ln \left ( 1+x \right ) + \left ( {\it \_C1}-2 \right ) x+{\it \_C1}-3 \right \} \] 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*(1+x)^2*diff(diff(y(x),x),x)-(1+x)*diff(y(x),x)+y(x) = x, y(x),'implicit')
Maple raw output
y(x) = (1+x)^(1/2)*_C2+(1+x)*ln(1+x)+(_C1-2)*x+_C1-3