7.10.1 problem 1

Internal problem ID [271]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 1
Date solved : Monday, January 27, 2025 at 02:43:09 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)-4*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_1 e^{4 x}+c_2\right ) \]