8.9.1 problem 1

Internal problem ID [845]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 1
Date solved : Monday, January 27, 2025 at 03:09:52 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (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: 0.012 (sec). Leaf size: 22

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

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