ODE
\[ (x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.186771 (sec), leaf count = 31
\[\left \{\left \{y(x)\to c_2 (x+1)^3+c_1 (x+1)^2+\frac {1}{6} (3 x+2)\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) = \left ( 1+x \right ) ^{2}{\it \_C2}+ \left ( 1+x \right ) ^{3}{\it \_C1}-{\frac {{x}^{2}}{3}}-{\frac {x}{6}} \right \} \] Mathematica raw input
DSolve[6*y[x] - 4*(1 + x)*y'[x] + (1 + x)^2*y''[x] == x,y[x],x]
Mathematica raw output
{{y[x] -> (2 + 3*x)/6 + (1 + x)^2*C[1] + (1 + x)^3*C[2]}}
Maple raw input
dsolve((1+x)^2*diff(diff(y(x),x),x)-4*(1+x)*diff(y(x),x)+6*y(x) = x, y(x),'implicit')
Maple raw output
y(x) = (1+x)^2*_C2+(1+x)^3*_C1-1/3*x^2-1/6*x