78.10.1 problem 1

Internal problem ID [18262]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 15. The General Solution of the Homogeneous Equation. Problems at page 117
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 11:44:41 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 20

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

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