59.1.1 problem 5.1 (i)

Internal problem ID [14985]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.1 (i)
Date solved : Thursday, October 02, 2025 at 09:58:05 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(x(t),t) = sin(t)+cos(t); 
dsolve(ode,x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.071 (sec). Leaf size: 10

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

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