20.1.17 problem Problem 23

Internal problem ID [3574]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 23
Date solved : Tuesday, March 04, 2025 at 04:52:10 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

ode=D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} (c_2 x+c_1) \]

✓ Sympy. Time used: 0.152 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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