49.9.9 problem 5(b)

Internal problem ID [7658]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 83
Problem number : 5(b)
Date solved : Monday, January 27, 2025 at 03:09:07 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-k^{4} y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.071 (sec). Leaf size: 5

dsolve([diff(y(x),x$4)-k^4*y(x)=0,y(0) = 0, D(y)(0) = 0, y(1) = 0, D(y)(1) = 0],y(x), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 6

DSolve[{D[y[x],{x,4}]-k^4*y[x]==0,{y[0]==0,y[1]==0,Derivative[1][y][0] ==0,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 0 \]