65.1.1 problem 5.1 (i)

Internal problem ID [13704]
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 : Tuesday, January 28, 2025 at 05:55:40 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 22

DSolve[D[x[t],t]==Sin[t]+Cos[t],x[t],t,IncludeSingularSolutions -> True]
 

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