15.1.12 problem 12

Internal problem ID [2852]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 12
Date solved : Monday, January 27, 2025 at 06:19:59 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=1-\sin \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve(diff(x(t),t)=1-sin(2*t),x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\cos \left (2 t \right )}{2}+t +c_1 \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 17

DSolve[D[x[t],t]==1-Sin[2*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to t+\frac {1}{2} \cos (2 t)+c_1 \]