42.4.9 problem Problem 3.12

Internal problem ID [8837]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.12
Date solved : Tuesday, September 30, 2025 at 05:53:30 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 10

ode:=diff(diff(u(theta),theta),theta)-cot(theta)*diff(u(theta),theta) = 0; 
dsolve(ode,u(theta), singsol=all);
 

\[ u = c_1 +\cos \left (\theta \right ) c_2 \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 13

ode=D[ u[\[Theta]], { \[Theta],2} ]-Cot[\[Theta]]*D[ u[\[Theta]],  \[Theta] ]==0; 
ic={}; 
DSolve[{ode,ic},u[\[Theta]],\[Theta],IncludeSingularSolutions->True]
 

\begin{align*} u(\theta )&\to c_2 \cos (\theta )+c_1 \end{align*}

✓ Sympy. Time used: 0.114 (sec). Leaf size: 8

from sympy import * 
theta = symbols("theta") 
u = Function("u") 
ode = Eq(Derivative(u(theta), (theta, 2)) - Derivative(u(theta), theta)/tan(theta),0) 
ics = {} 
dsolve(ode,func=u(theta),ics=ics)
 

\[ u{\left (\theta \right )} = C_{1} + C_{2} \cos {\left (\theta \right )} \]