63.5.17 problem 3(e)

Internal problem ID [13091]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 3(e)
Date solved : Tuesday, January 28, 2025 at 04:51:59 AM
CAS classification : [_separable]

\begin{align*} \cos \left (\theta \right ) v^{\prime }+v&=3 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(cos(theta)*diff(v(theta),theta)+v(theta)=3,v(theta), singsol=all)
 

\[ v = \frac {\left (c_{1} +6\right ) \cos \left (\frac {\theta }{2}\right )-c_{1} \sin \left (\frac {\theta }{2}\right )}{\cos \left (\frac {\theta }{2}\right )+\sin \left (\frac {\theta }{2}\right )} \]

✓ Solution by Mathematica

Time used: 0.087 (sec). Leaf size: 26

DSolve[Cos[theta]*D[v[theta],theta]+v[theta]==3,v[theta],theta,IncludeSingularSolutions -> True]
 

\begin{align*} v(\theta )\to 3+c_1 e^{-2 \text {arctanh}\left (\tan \left (\frac {\theta }{2}\right )\right )} \\ v(\theta )\to 3 \\ \end{align*}