Internal problem ID [15461]
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: 717.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+\lambda ^{2} y=0} \] With initial conditions \begin {align*} [y^{\prime }\left (0\right ) = 0, y^{\prime }\left (\pi \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 5
dsolve([diff(y(x),x$2)+lambda^2*y(x)=0,D(y)(0) = 0, D(y)(Pi) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
DSolve[{y''[x]+\[Lambda]^2*y[x]==0,{y'[0]==0,y'[Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} c_1 \cos \left (x \sqrt {\lambda ^2}\right ) & \unicode {f80d}\in \mathbb {Z}\land \unicode {f80d}\geq 0\land \lambda ^2=\unicode {f80d}^2 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]