1.8.1 problem 1

Internal problem ID [215]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 03:53:42 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 )&=0 \\ y^{\prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 8

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

\[ y = 5 \sinh \left (x \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {5}{2} e^{-x} \left (e^{2 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.035 (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): 0, Subs(Derivative(y(x), x), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

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