7.1.8 problem 8

Internal problem ID [8]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.2. Problems at page 17
Problem number : 8
Date solved : Friday, February 07, 2025 at 08:11:46 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\cos \left (2 x \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

dsolve([diff(y(x),x)=cos(2*x),y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {\sin \left (2 x \right )}{2}+1 \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 12

DSolve[{D[y[x],x]==Cos[2*x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (x) \cos (x)+1 \]