89.11.4 problem 4

Internal problem ID [24529]
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 : 4
Date solved : Thursday, October 02, 2025 at 10:45:55 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+5*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{x}+c_2 \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

ode=D[y[x],{x,2}] +5* D[y[x],{x,1}] +6*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (c_2 e^x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) + 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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