64.5.11 problem 11

Internal problem ID [13324]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 05:22:12 AM
CAS classification : [_linear]

\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 10

dsolve(diff(r(t),t)+r(t)*tan(t)=cos(t),r(t), singsol=all)
 

\[ r = \left (t +c_{1} \right ) \cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 12

DSolve[D[r[t],t]+r[t]*Tan[t]==Cos[t],r[t],t,IncludeSingularSolutions -> True]
 

\[ r(t)\to (t+c_1) \cos (t) \]