69.22.4 problem 708 (b)

Internal problem ID [18470]
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 (b)
Date solved : Thursday, October 02, 2025 at 03:13:53 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 \left (2 \pi \right )&=1 \\ \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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]
 

{}

✗ Sympy

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)
 

ValueError : Couldnt solve for initial conditions