65.1.1 problem 5.1 (i)

Internal problem ID [13633]
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 : Monday, March 31, 2025 at 08:03:24 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: 0.005 (sec). Leaf size: 22

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

\[ x(t)\to \int _1^t(\cos (K[1])+\sin (K[1]))dK[1]+c_1 \]

✓ Sympy. Time used: 0.118 (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)
 

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