44.13.10 problem 10

Internal problem ID [9311]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 06:16:20 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+2*a^2*diff(diff(y(x),x),x)+a^4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 x +c_2 \right ) \cos \left (a x \right )+\sin \left (a x \right ) \left (c_3 x +c_1 \right ) \]

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

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

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

✓ Sympy. Time used: 0.077 (sec). Leaf size: 26

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

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