Internal problem ID [4066]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.3, page 220.
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: 0.001 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)-y(x)=0,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]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x+c_2 e^{-x} \\ \end{align*}