Internal problem ID [5130]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 10
dsolve(diff(u(theta),theta$2)-cot(theta)*diff(u(theta),theta)=0,u(theta), singsol=all)
\[ u \left (\theta \right ) = c_{1}+\cos \left (\theta \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 13
DSolve[u''[\[Theta]]-Cot[\[Theta]]*u'[\[Theta]]==0,u[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} u(\theta )\to c_2 \cos (\theta )+c_1 \\ \end{align*}