66.13.1 problem 1

Internal problem ID [16149]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.6 page 342
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:42:58 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = c_1 \,{\mathrm e}^{-t}+c_2 \,{\mathrm e}^{7 t} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to e^{-t} \left (c_2 e^{8 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = C_{1} e^{- t} + C_{2} e^{7 t} \]