64.23.4 problem 4

Internal problem ID [13681]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 12, Sturm-Liouville problems. Section 12.1, Exercises page 596
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 05:55:03 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 5

dsolve([diff(y(x),x$2)+lambda*y(x)=0,D(y)(0) = 0, D(y)(L) = 0],y(x), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 42

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

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