43.7.5 problem 4(f)

Internal problem ID [8930]
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(f)
Date solved : Tuesday, September 30, 2025 at 06:00:16 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+5*diff(diff(y(x),x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 30

ode=D[y[x],{x,4}]+5*D[y[x],{x,2}]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \cos (2 x)+c_4 \sin (x)+\cos (x) (2 c_2 \sin (x)+c_3) \end{align*}

✓ Sympy. Time used: 0.041 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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