23.3.139 problem 141

Internal problem ID [5853]
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 : 141
Date solved : Tuesday, September 30, 2025 at 02:04:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

ode:=3*y(x)+2*cot(x)*diff(y(x),x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (2 c_2 \cot \left (x \right )+2 c_1 \right ) \cos \left (x \right )-c_2 \csc \left (x \right ) \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 42

ode=3*y[x] + 2*Cot[x]*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 e^{3 i x}}{2 \left (-1+e^{2 i x}\right )}+c_1 e^{-2 i x} \csc (x) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) + Derivative(y(x), (x, 2)) + 2*Derivative(y(x), x)/tan(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE (3*y(x) + Derivative(y(x), (x, 2)))*tan(x)/2 + Derivative(y(x),