ODE
\[ 4 x y''(x)+4 \coth (x) y'(x)+y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.611336 (sec), leaf count = 0 , could not solve
DSolve[y[x] + 4*Coth[x]*Derivative[1][y][x] + 4*x*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 1.12 (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac {{\rm coth} \left (x\right ){\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{x}}+{\frac {{\it \_Y} \left ( x \right ) }{4\,x}} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]
Mathematica raw input
DSolve[y[x] + 4*Coth[x]*y'[x] + 4*x*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[y[x] + 4*Coth[x]*Derivative[1][y][x] + 4*x*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(4*x*diff(diff(y(x),x),x)+4*diff(y(x),x)*coth(x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = DESol({diff(diff(_Y(x),x),x)+coth(x)/x*diff(_Y(x),x)+1/4/x*_Y(x)},{_Y(x)})