78.7.3 problem 1 (c)

Internal problem ID [18189]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 11 (Reduction of order). Problems at page 87
Problem number : 1 (c)
Date solved : Tuesday, January 28, 2025 at 11:37:35 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 31

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

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