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 = 0.0285268 (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 = 0.009 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sinh \left ( \left ( a-x \right ) ^{-1} \right ) +{\it \_C2}\,\cosh \left ( \left ( a-x \right ) ^{-1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*sinh(1/(a-x))+_C2*cosh(1/(a-x))