50.16.2 problem 2

Internal problem ID [8070]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Problems for Discussion and Exploration. Page 105
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:41:28 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=-3 y \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)=-3*y(x),y(0) = -1],y(x), singsol=all)
 

\[ y = c_{1} \sin \left (\sqrt {3}\, x \right )-\cos \left (\sqrt {3}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 27

DSolve[{D[y[x],{x,2}]==-3*y[x],{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \]