26.7.10 problem Exercise 20.11, page 220

Internal problem ID [7060]
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 : Tuesday, September 30, 2025 at 04:21:02 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 34

ode:=diff(diff(y(x),x),x)-2*k*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 44

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

\begin{align*} 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} \end{align*}

✓ Sympy. Time used: 0.123 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
k = symbols("k") 
y = Function("y") 
ode = Eq(-2*k*Derivative(y(x), x) - 2*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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