48.4.9 problem Problem 3.12

Internal problem ID [7551]
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 : Monday, January 27, 2025 at 03:05:36 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 10

dsolve(diff(u(theta),theta$2)-cot(theta)*diff(u(theta),theta)=0,u(theta), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 13

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

\[ u(\theta )\to c_2 \cos (\theta )+c_1 \]