23.3.140 problem 142

Internal problem ID [5854]
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 : 142
Date solved : Tuesday, September 30, 2025 at 02:04:24 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 29

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

\[ y = \left (2 c_1 \cos \left (x \right )^{2}+2 c_2 \sin \left (x \right ) \cos \left (x \right )+\frac {{\mathrm e}^{x}}{5}-c_1 \right ) \csc \left (x \right ) \]

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 56

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

\begin{align*} y(x)&\to \frac {e^{-i x} \left (4 i e^{(1+2 i) x}+5 c_2 e^{4 i x}+20 i c_1\right )}{10 \left (-1+e^{2 i x}\right )} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - exp(x)/sin(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)*tan(x)/2 - exp(x)/(2*cos(x)) + tan(x)*Derivative(y(x), (x