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 : Sunday, March 30, 2025 at 12:18:15 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*}

✓ Maple. Time used: 0.104 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]

✓ Sympy. Time used: 0.544 (sec). Leaf size: 3

from sympy import * 
x = symbols("x") 
k = symbols("k") 
y = Function("y") 
ode = Eq(-k**4*y(x) + Derivative(y(x), (x, 4)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 0, y(1): 0, Subs(Derivative(y(x), x), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 0 \]