50.1.26 problem 3(b)

Internal problem ID [7798]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 3(b)
Date solved : Monday, January 27, 2025 at 03:23:23 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=2 \sin \left (x \right ) \cos \left (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)=2*sin(x)*cos(x),y(0) = 1],y(x), singsol=all)
 

\[ y = -\frac {\cos \left (2 x \right )}{2}+\frac {3}{2} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 17

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

\[ y(x)\to \frac {1}{2} (3-\cos (2 x)) \]