Internal problem ID [11649]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )=\cos \left (t \right )^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(cos(t)*diff(r(t),t)+(r(t)*sin(t)-cos(t)^4)=0,r(t), singsol=all)
\[ r \left (t \right ) = \frac {\left (2 t +\sin \left (2 t \right )+4 c_{1} \right ) \cos \left (t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 22
DSolve[Cos[t]*r'[t]+(r[t]*Sin[t]-Cos[t]^4)==0,r[t],t,IncludeSingularSolutions -> True]
\[ r(t)\to \frac {1}{2} \cos (t) (t+\sin (t) \cos (t)+2 c_1) \]