69.1.41 problem 60

Internal problem ID [14194]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 60
Date solved : Tuesday, January 28, 2025 at 06:21:27 AM
CAS classification : [_linear]

\begin{align*} s^{\prime } \cos \left (t \right )+s \sin \left (t \right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

dsolve(diff(s(t),t)*cos(t)+s(t)*sin(t)=1,s(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 13

DSolve[D[s[t],t]*Cos[t]+s[t]*Sin[t]==1,s[t],t,IncludeSingularSolutions -> True]
 

\[ s(t)\to \sin (t)+c_1 \cos (t) \]