69.1.42 problem 61

Internal problem ID [14195]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 61
Date solved : Tuesday, January 28, 2025 at 06:21:30 AM
CAS classification : [_linear]

\begin{align*} s^{\prime }+s \cos \left (t \right )&=\frac {\sin \left (2 t \right )}{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(diff(s(t),t)+s(t)*cos(t)=1/2*sin(2*t),s(t), singsol=all)
 

\[ s = \sin \left (t \right )-1+{\mathrm e}^{-\sin \left (t \right )} c_{1} \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 54

DSolve[D[s[t],t]+s[t]*Cos[t]==1/2*Sin[2*t],s[t],t,IncludeSingularSolutions -> True]
 

\[ s(t)\to \exp \left (\int _1^t-\cos (K[1])dK[1]\right ) \left (\int _1^t\exp \left (-\int _1^{K[2]}-\cos (K[1])dK[1]\right ) \cos (K[2]) \sin (K[2])dK[2]+c_1\right ) \]