8.1.8 problem 8

Internal problem ID [658]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 8
Date solved : Monday, January 27, 2025 at 02:56:47 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: 0.006 (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: 0.004 (sec). Leaf size: 12

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

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