80.8.5 problem 5

Internal problem ID [18513]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 5
Date solved : Monday, March 31, 2025 at 05:40:56 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 30

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 53

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

\[ y(x)\to c_2 e^{-\sqrt {a} x}+c_4 e^{\sqrt {a} x}+c_1 \cos \left (\sqrt {a} x\right )+c_3 \sin \left (\sqrt {a} x\right ) \]

✓ Sympy. Time used: 0.131 (sec). Leaf size: 32

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

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