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 = 0.654448 (sec), leaf count = 20
\[\left \{\left \{y(x)\to (x+1)^2 \left (c_2 (x+1)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) = \left ( 1+x \right ) ^{2} \left ( {\it \_C1}+{\it \_C2}\, \left ( 1+x \right ) \right ) \right \} \] 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((1+x)^2*diff(diff(y(x),x),x)-4*(1+x)*diff(y(x),x)+6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (1+x)^2*(_C1+_C2*(1+x))