89.11.3 problem 3

Internal problem ID [24528]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:45:55 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 22

ode=D[y[x],{x,2}] - D[y[x],{x,1}] -6*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.079 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{3 x} \]