32.7.3 problem Exercise 20.3, page 220

Internal problem ID [5918]
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
Date solved : Monday, January 27, 2025 at 01:27:28 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)-y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

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

\[ y(x)\to c_1 e^x+c_2 e^{-x} \]