Internal problem ID [6079]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES
Page 324
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\beta ^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+beta^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\beta x \right )+c_{2} \cos \left (\beta x \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 20
DSolve[y''[x]+\[Beta]^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (\beta x)+c_2 \sin (\beta x) \\ \end{align*}