68.15.61 problem 64 (a)

Internal problem ID [17787]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 64 (a)
Date solved : Thursday, October 02, 2025 at 02:28:16 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=x^3*diff(diff(diff(y(x),x),x),x)+16*x^2*diff(diff(y(x),x),x)+79*x*diff(y(x),x)+125*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \sin \left (3 \ln \left (x \right )\right ) x +c_3 \cos \left (3 \ln \left (x \right )\right ) x +c_1}{x^{5}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 30

ode=x^3*D[y[x],{x,3}]+16*x^2*D[y[x],{x,2}]+79*x*D[y[x],x]+125*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 x \cos (3 \log (x))+c_1 x \sin (3 \log (x))+c_3}{x^5} \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 16*x**2*Derivative(y(x), (x, 2)) + 79*x*Derivative(y(x), x) + 125*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\frac {C_{1}}{x} + C_{2} \sin {\left (3 \log {\left (x \right )} \right )} + C_{3} \cos {\left (3 \log {\left (x \right )} \right )}}{x^{4}} \]