38.2.13 problem 13

Internal problem ID [8231]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 05:19:21 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (-1\right )&=5 \\ y^{\prime }\left (-1\right )&=-5 \\ \end{align*}

✓ Maple. Time used: 0.057 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)-y(x) = 0; 
ic:=[y(-1) = 5, D(y)(-1) = -5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{-1-x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 14

ode=D[y[x],{x,2}]-y[x]==0; 
ic={y[-1]==5,Derivative[1][y][-1] == -5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.040 (sec). Leaf size: 10

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

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