68.18.14 problem 20

Internal problem ID [17858]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 20
Date solved : Thursday, October 02, 2025 at 02:28:56 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 12 y^{\prime \prime }+8 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=12*diff(diff(y(x),x),x)+8*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {x}{6}}+c_2 \,{\mathrm e}^{-\frac {x}{2}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 26

ode=12*D[y[x],{x,2}]+8*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x/2} \left (c_1 e^{x/3}+c_2\right ) \end{align*}

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

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 8*Derivative(y(x), x) + 12*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {x}{2}} + C_{2} e^{- \frac {x}{6}} \]