38.2.12 problem 12

Internal problem ID [8230]
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 : 12
Date solved : Tuesday, September 30, 2025 at 05:19:19 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 )&=0 \\ y^{\prime }\left (1\right )&={\mathrm e} \\ \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 17

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

\[ y = \frac {{\mathrm e}^{x}}{2}-\frac {{\mathrm e}^{2-x}}{2} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {e^x}{2}-\frac {e^{2-x}}{2} \end{align*}

✓ Sympy. Time used: 0.041 (sec). Leaf size: 15

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

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