15.9.7 problem 21

Internal problem ID [3064]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 21
Date solved : Monday, January 27, 2025 at 07:19:02 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

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

\[ y = c_{1} {\mathrm e}^{\left (1+\sqrt {2}\right ) x}+c_2 \,{\mathrm e}^{-\left (\sqrt {2}-1\right ) x} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 34

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

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