88.14.3 problem 3

Internal problem ID [24091]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 93
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:59:08 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-4 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{2 x \sqrt {5}}+c_2 \right ) {\mathrm e}^{-\left (\sqrt {5}-1\right ) x} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 34

ode=D[y[x],{x,2}]-2*D[y[x],x]-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.101 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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