13.7.1 problem 1

Internal problem ID [2364]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2, linear equations with constant coefficients. Page 138
Problem number : 1
Date solved : Monday, January 27, 2025 at 05:50:17 AM
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(t),t$2)-y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t} c_1 +c_2 \,{\mathrm e}^{t} \]

✓ Solution by Mathematica

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

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

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