ODE
\[ x^2 (x+1) y''(x)+x y'(x)+(x+1)^3 (-y(x))=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.178339 (sec), leaf count = 25
\[\{\{y(x)\to c_1 \cosh (x+\log (x))+i c_2 \sinh (x+\log (x))\}\}\]
Maple ✓
cpu = 0.064 (sec), leaf count = 19
\[[y \left (x \right ) = \textit {\_C1} \sinh \left (x +\ln \left (x \right )\right )+\textit {\_C2} \cosh \left (x +\ln \left (x \right )\right )]\] Mathematica raw input
DSolve[-((1 + x)^3*y[x]) + x*y'[x] + x^2*(1 + x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cosh[x + Log[x]] + I*C[2]*Sinh[x + Log[x]]}}
Maple raw input
dsolve(x^2*(x+1)*diff(diff(y(x),x),x)+x*diff(y(x),x)-(x+1)^3*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*sinh(x+ln(x))+_C2*cosh(x+ln(x))]