Internal problem ID [11660]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {r^{\prime }+r \tan \left (t \right )=\cos \left (t \right )^{2}} \] With initial conditions \begin {align*} \left [r \left (\frac {\pi }{4}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(r(t),t)+r(t)*tan(t)=cos(t)^2,r(1/4*Pi) = 1],r(t), singsol=all)
\[ r \left (t \right ) = \frac {\left (2 \sin \left (t \right )+\sqrt {2}\right ) \cos \left (t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 16
DSolve[{r'[t]+r[t]*Tan[t]==Cos[t]^2,{r[Pi/4]==1}},r[t],t,IncludeSingularSolutions -> True]
\[ r(t)\to \left (\sin (t)+\frac {1}{\sqrt {2}}\right ) \cos (t) \]