ODE
\[ (x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.171482 (sec), leaf count = 20
\[\left \{\left \{y(x)\to (x+1)^2 (c_2 (x+1)+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 19
\[[y \left (x \right ) = \left (x +1\right )^{2} \textit {\_C1} +\textit {\_C2} \left (x +1\right )^{3}]\] Mathematica raw input
DSolve[6*y[x] - 4*(1 + x)*y'[x] + (1 + x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 + x)^2*(C[1] + (1 + x)*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) = 0, y(x))
Maple raw output
[y(x) = (x+1)^2*_C1+_C2*(x+1)^3]