1.10.6 problem 6

Internal problem ID [276]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 03:54:30 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+5 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)+5*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{x \sqrt {5}}+c_2 \right ) {\mathrm e}^{-\frac {\left (5+\sqrt {5}\right ) x}{2}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 35

ode=D[y[x],{x,2}]+5*D[y[x],x]+5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\frac {1}{2} \left (5+\sqrt {5}\right ) x} \left (c_2 e^{\sqrt {5} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) + 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (-5 + \sqrt {5}\right )}{2}} + C_{2} e^{- \frac {x \left (\sqrt {5} + 5\right )}{2}} \]