71.2.10 problem 8 b(i)

Internal problem ID [14271]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 8 b(i)
Date solved : Monday, March 31, 2025 at 12:14:57 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.114 (sec). Leaf size: 18

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

\[ y = -\operatorname {csch}\left (3\right ) \sinh \left (-3+\frac {3 x}{2}\right ) {\mathrm e}^{\frac {x}{2}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 29

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

\[ y(x)\to \frac {e^{-x} \left (e^6-e^{3 x}\right )}{e^6-1} \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = - \frac {e^{2 x}}{-1 + e^{6}} + \frac {e^{6} e^{- x}}{-1 + e^{6}} \]