43.7.2 problem 4(b)

Internal problem ID [8927]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 74
Problem number : 4(b)
Date solved : Tuesday, September 30, 2025 at 06:00:15 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 65

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -c_1 \,{\mathrm e}^{-\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )-c_2 \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+c_3 \,{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right )+c_4 \,{\mathrm e}^{\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 67

ode=D[y[x],{x,4}]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\sqrt {2} x} \left (\left (c_1 e^{2 \sqrt {2} x}+c_2\right ) \cos \left (\sqrt {2} x\right )+\left (c_4 e^{2 \sqrt {2} x}+c_3\right ) \sin \left (\sqrt {2} x\right )\right ) \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 60

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (\sqrt {2} x \right )} + C_{2} \cos {\left (\sqrt {2} x \right )}\right ) e^{- \sqrt {2} x} + \left (C_{3} \sin {\left (\sqrt {2} x \right )} + C_{4} \cos {\left (\sqrt {2} x \right )}\right ) e^{\sqrt {2} x} \]