64.5.23 problem 23

Internal problem ID [13336]
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 : 23
Date solved : Tuesday, January 28, 2025 at 05:22:46 AM
CAS classification : [_linear]

\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \end{align*}

With initial conditions

\begin{align*} r \left (\frac {\pi }{4}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 16

dsolve([diff(r(t),t)+r(t)*tan(t)=cos(t)^2,r(1/4*Pi) = 1],r(t), singsol=all)
 

\[ r = \frac {\left (2 \sin \left (t \right )+\sqrt {2}\right ) \cos \left (t \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 28

DSolve[{D[r[t],t]+r[t]*Tan[t]==Cos[t]^2,{r[Pi/4]==1}},r[t],t,IncludeSingularSolutions -> True]
 

\[ r(t)\to \cos (t) \left (\int _{\frac {\pi }{4}}^t\cos (K[1])dK[1]+\sqrt {2}\right ) \]