63.1.41 problem 60

Internal problem ID [15481]
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 : Thursday, October 02, 2025 at 10:18:21 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ s = \cos \left (t \right ) c_1 +\sin \left (t \right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 13

ode=D[s[t],t]*Cos[t]+s[t]*Sin[t]==1; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to \sin (t)+c_1 \cos (t) \end{align*}

✓ Sympy. Time used: 0.428 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(s(t)*sin(t) + cos(t)*Derivative(s(t), t) - 1,0) 
ics = {} 
dsolve(ode,func=s(t),ics=ics)
 

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