Internal problem ID [15452]
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 ODE’s). Section 17. Boundary value problems. Exercises page
163
Problem number: 708 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y \left (2 \pi \right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 27
dsolve([diff(y(x),x$2)-y(x)=0,y(0) = 0, y(2*Pi) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-x +2 \pi } \left ({\mathrm e}^{2 x}-1\right )}{{\mathrm e}^{4 \pi }-1} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 31
DSolve[{y''[x]-y[x]==0,{y[0]==0,y[2*Pi]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{2 \pi -x} \left (e^{2 x}-1\right )}{e^{4 \pi }-1} \]