30.12.16 problem 16

Internal problem ID [7608]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 04:54:53 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=3 \\ y^{\prime }\left (-1\right )&=9 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 19

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)-5*y(t) = 0; 
ic:=[y(-1) = 3, D(y)(-1) = 9]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{5+5 t}+{\mathrm e}^{-1-t} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 22

ode=D[y[t],{t,2}]-4*D[y[t],t]-5*y[t]==0; 
ic={y[-1]==3,Derivative[1][y][-1] ==9}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t-1}+2 e^{5 t+5} \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-5*y(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(-1): 3, Subs(Derivative(y(t), t), t, -1): 9} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{5} e^{5 t} + \frac {e^{- t}}{e} \]