64.2.7 problem 4(c)

Internal problem ID [13267]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, section 1.3. Exercises page 22
Problem number : 4(c)
Date solved : Tuesday, January 28, 2025 at 05:13:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 8

dsolve([diff(y(x),x$2)+y(x)=0,y(0) = 0, D(y)(Pi) = 1],y(x), singsol=all)
 

\[ y = -\sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 9

DSolve[{D[y[x],{x,2}]+y[x]==0,{y[0]==0,Derivative[1][y][Pi]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sin (x) \]