8.7.2 problem 2

Internal problem ID [2546]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2. Linear equations with constant coefficients. Excercises page 140
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 05:46:59 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=6*diff(diff(y(t),t),t)-7*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

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

ode=6*D[y[t],{t,2}]-7*D[y[t],t]+y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 e^{t/6}+c_2 e^t \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 7*Derivative(y(t), t) + 6*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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