75.22.3 problem 708 (a)

Internal problem ID [17103]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 17. Boundary value problems. Exercises page 163
Problem number : 708 (a)
Date solved : Thursday, March 13, 2025 at 09:16:02 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 \left (2 \pi \right )&=1 \end{align*}

✓ Maple. Time used: 0.249 (sec). Leaf size: 27

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

\[ y = \frac {{\mathrm e}^{-x +2 \pi } \left ({\mathrm e}^{2 x}-1\right )}{{\mathrm e}^{4 \pi }-1} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 31

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

\[ y(x)\to \frac {e^{2 \pi -x} \left (e^{2 x}-1\right )}{e^{4 \pi }-1} \]

✓ Sympy. Time used: 0.077 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = \frac {e^{2 \pi } e^{x}}{-1 + e^{4 \pi }} - \frac {e^{2 \pi } e^{- x}}{-1 + e^{4 \pi }} \]