64.5.12 problem 12

Internal problem ID [13325]
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 : 12
Date solved : Tuesday, January 28, 2025 at 05:22:14 AM
CAS classification : [_linear]

\begin{align*} \cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(cos(t)*diff(r(t),t)+(r(t)*sin(t)-cos(t)^4)=0,r(t), singsol=all)
 

\[ r = \frac {\left (2 t +\sin \left (2 t \right )+4 c_{1} \right ) \cos \left (t \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 23

DSolve[Cos[t]*D[r[t],t]+(r[t]*Sin[t]-Cos[t]^4)==0,r[t],t,IncludeSingularSolutions -> True]
 

\[ r(t)\to \cos (t) \left (\int _1^t\cos ^2(K[1])dK[1]+c_1\right ) \]