64.13.13 problem 13

Internal problem ID [13472]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 13
Date solved : Monday, March 31, 2025 at 07:58:52 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y&=0 \end{align*}

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

ode:=x^3*diff(diff(diff(y(x),x),x),x)-x^2*diff(diff(y(x),x),x)-6*x*diff(y(x),x)+18*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_3 \,x^{5} \ln \left (x \right )+c_2 \,x^{5}+c_1}{x^{2}} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 26

ode=x^3*D[y[x],{x,3}]-x^2*D[y[x],{x,2}]-6*x*D[y[x],x]+18*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 x^5+c_3 x^5 \log (x)+c_1}{x^2} \]

✓ Sympy. Time used: 0.193 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - x**2*Derivative(y(x), (x, 2)) - 6*x*Derivative(y(x), x) + 18*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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