Internal problem ID [5129]
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 3.11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 16
dsolve(diff(phi(theta),theta)-1/2*phi(theta)^2-phi(theta)*cot(theta)=0,phi(theta), singsol=all)
\[ \phi \left (\theta \right ) = \frac {2 \sin \left (\theta \right )}{\cos \left (\theta \right )+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.301 (sec). Leaf size: 23
DSolve[\[Phi]'[\[Theta]]-1/2*\[Phi][\[Theta]]^2-\[Phi][\[Theta]]*Cot[\[Theta]]==0,\[Phi][\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} \phi (\theta )\to \frac {2 \sin (\theta )}{\cos (\theta )+2 c_1} \\ \phi (\theta )\to 0 \\ \end{align*}