82.45.1 problem Ex. 1

Internal problem ID [18898]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 100
Problem number : Ex. 1
Date solved : Monday, March 31, 2025 at 06:21:20 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: 0.005 (sec). Leaf size: 21

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);
 

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

✓ Mathematica. Time used: 0.133 (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]
 

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

✓ Sympy. Time used: 0.081 (sec). Leaf size: 24

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)
 

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