32.7.10 problem Exercise 20.11, page 220

Internal problem ID [5925]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.11, page 220
Date solved : Monday, January 27, 2025 at 01:27:35 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 44

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

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