87.13.30 problem 34

Internal problem ID [23513]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 34
Date solved : Thursday, October 02, 2025 at 09:42:36 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime \prime }-\frac {6 y}{x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=x*diff(diff(diff(y(x),x),x),x)-6/x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{3}+c_2 \sin \left (\sqrt {2}\, \ln \left (x \right )\right )+c_3 \cos \left (\sqrt {2}\, \ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 36

ode=x*D[y[x],{x,3}]-6/x^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 x^3+c_1 \cos \left (\sqrt {2} \log (x)\right )+c_2 \sin \left (\sqrt {2} \log (x)\right ) \end{align*}

✓ Sympy. Time used: 0.076 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) - 6*y(x)/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {x} \left (C_{1} I_{1}\left (\frac {2 \sqrt {6}}{\sqrt {x}}\right ) + C_{2} Y_{1}\left (- \frac {2 \sqrt {6} i}{\sqrt {x}}\right )\right ) \]