64.23.2 problem 2

Internal problem ID [13679]
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 : 2
Date solved : Tuesday, January 28, 2025 at 05:54:56 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

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

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} c_1 \sin \left (x \sqrt {\lambda }\right ) & \unicode {f80d}\in \mathbb {Z}\land \unicode {f80d}\geq 1\land \lambda =\left (\unicode {f80d}-\frac {1}{2}\right )^2 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]