79.1.5 problem 1 (v)

Internal problem ID [18492]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 1 (v)
Date solved : Tuesday, January 28, 2025 at 11:50:51 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} x \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 11

dsolve([diff(x(t),t)=cos(t),x(1) = 0],x(t), singsol=all)
 

\[ x = \sin \left (t \right )-\sin \left (1\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 12

DSolve[{D[x[t],t]==Cos[t],{x[1]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \sin (t)-\sin (1) \]