Internal problem ID [4393]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page
564
Problem number: 5, using elementary method.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)=y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 20
DSolve[y''[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x+c_2 e^{-x} \\ \end{align*}