Internal problem ID [5649]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)=-3*y(x),y(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\sqrt {3}\, x \right )-\cos \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 27
DSolve[{y''[x]==-3*y[x],{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \\ \end{align*}