44.2.11 problem 11

Internal problem ID [6943]
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 : 11
Date solved : Sunday, March 30, 2025 at 11:30:22 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-x}}{2}+\frac {3 \,{\mathrm e}^{x}}{2} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 22

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

\[ y(x)\to \frac {3 e^x}{2}-\frac {e^{-x}}{2} \]

✓ Sympy. Time used: 0.111 (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(0): 1, Subs(Derivative(y(x), x), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 e^{x}}{2} - \frac {e^{- x}}{2} \]