75.22.12 problem 717

Internal problem ID [17191]
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 : 717
Date solved : Tuesday, January 28, 2025 at 09:56:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\lambda ^{2} y&=0 \end{align*}

With initial conditions

\begin{align*} y^{\prime }\left (0\right )&=0\\ y^{\prime }\left (\pi \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (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)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 36

DSolve[{D[y[x],{x,2}]+\[Lambda]^2*y[x]==0,{Derivative[1][y][0] ==0,Derivative[1][y][Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} c_1 \cos \left (x \sqrt {\lambda ^2}\right ) & \unicode {f80d}\in \mathbb {Z}\land \unicode {f80d}\geq 0\land \lambda ^2=\unicode {f80d}^2 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]