ODE
\[ (a-x)^4 y''(x)-2 (a-x)^3 y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.197506 (sec), leaf count = 31
\[\left \{\left \{y(x)\to c_1 \cosh \left (\frac {1}{a-x}\right )+i c_2 \sinh \left (\frac {1}{a-x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.044 (sec), leaf count = 25
\[\left [y \left (x \right ) = \textit {\_C1} \sinh \left (\frac {1}{a -x}\right )+\textit {\_C2} \cosh \left (\frac {1}{a -x}\right )\right ]\] Mathematica raw input
DSolve[-y[x] - 2*(a - x)^3*y'[x] + (a - x)^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cosh[(a - x)^(-1)] + I*C[2]*Sinh[(a - x)^(-1)]}}
Maple raw input
dsolve((a-x)^4*diff(diff(y(x),x),x)-2*(a-x)^3*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*sinh(1/(a-x))+_C2*cosh(1/(a-x))]