71.5.3 problem 3

Internal problem ID [14399]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 06:29:44 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 10

dsolve([diff(y(x),x)=2*sin(x),y(Pi) = 1],y(x), singsol=all)
 

\[ y = -2 \cos \left (x \right )-1 \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 19

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

\[ y(x)\to \int _{\pi }^x2 \sin (K[1])dK[1]+1 \]