14.33.6 problem 9

Internal problem ID [2840]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 5. Separation of variables and Fourier series. Section 5.1 (Two point boundary-value problems). Page 480
Problem number : 9
Date solved : Monday, January 27, 2025 at 06:19:28 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 \left (1\right )&=0 \end{align*}

✓ Solution by Maple

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

dsolve([diff(y(t),t$2)+lambda*y(t)=0,y(0) = 0, y(1) = 0],y(t), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 36

DSolve[{D[y[t],{t,2}]-2*D[y[t],t]+(1+\[Lambda])*y[t]==0,{y[0] == 0,y[1] == 0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 2 e^t c_1 \sinh \left (t \sqrt {-\lambda }\right ) & \sinh \left (\sqrt {-\lambda }\right )=0 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]