23.3.239 problem 241

Internal problem ID [5953]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 241
Date solved : Tuesday, September 30, 2025 at 02:06:44 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y+4 \coth \left (x \right ) y^{\prime }+4 x y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=y(x)+4*coth(x)*diff(y(x),x)+4*x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x] + 4*Coth[x]*D[y[x],x] + 4*x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), (x, 2)) + y(x) + 4*Derivative(y(x), x)/tanh(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE (4*x*Derivative(y(x), (x, 2)) + y(x))*tanh(x)/4 + Derivative(y(x