58.1.9 problem 4(a)

Internal problem ID [14535]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 4(a)
Date solved : Thursday, October 02, 2025 at 09:38:22 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{4 x}+c_2 \,{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 22

ode=D[y[x],{x,2}]-2*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (c_2 e^{6 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{4 x} \]