82.48.5 problem Ex. 5

Internal problem ID [18907]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 5
Date solved : Thursday, March 13, 2025 at 01:11:18 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

\[ y \left (x \right ) = c_{1} +c_{2} x +c_3 \,{\mathrm e}^{a x}+c_4 \,{\mathrm e}^{-a x} \]

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 34

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

\[ y(x)\to \frac {c_1 e^{a x}+c_2 e^{-a x}}{a^2}+c_4 x+c_3 \]

✓ Sympy. Time used: 0.083 (sec). Leaf size: 20

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

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