75.22.3 problem 708 (a)

Internal problem ID [17182]
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 : Tuesday, January 28, 2025 at 09:56:23 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*}

✓ Solution by Maple

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

dsolve([diff(y(x),x$2)-y(x)=0,y(0) = 0, y(2*Pi) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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