71.9.11 problem 13

Internal problem ID [14411]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 13
Date solved : Saturday, February 22, 2025 at 03:47:25 PM
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 )&=1 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{2} e^{-x} \left (e^{2 x}-1\right ) \]

✓ Sympy. Time used: 0.069 (sec). Leaf size: 14

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): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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