78.11.2 problem 2 (b)

Internal problem ID [18273]
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 16. The Use of a Known Solution to find Another. Problems at page 121
Problem number : 2 (b)
Date solved : Tuesday, January 28, 2025 at 11:45:00 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 20

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

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