23.5.147 problem 147

Internal problem ID [6756]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 147
Date solved : Tuesday, September 30, 2025 at 03:51:26 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} a^{2} b^{2} y+\left (a^{2}+b^{2}\right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 29

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 0.096 (sec). Leaf size: 56

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

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