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 = 0.172046 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {1}{6} (3 x+2)+c_2 (x+1)^3+c_1 (x+1)^2\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 27
\[\left [y \left (x \right ) = \left (x +1\right )^{2} \textit {\_C2} +\left (x +1\right )^{3} \textit {\_C1} -\frac {x^{2}}{3}-\frac {x}{6}\right ]\] 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((x+1)^2*diff(diff(y(x),x),x)-4*(x+1)*diff(y(x),x)+6*y(x) = x, y(x))
Maple raw output
[y(x) = (x+1)^2*_C2+(x+1)^3*_C1-1/3*x^2-1/6*x]