43.16.5 problem 1(e)

Internal problem ID [8989]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 4. Linear equations with Regular Singular Points. Page 149
Problem number : 1(e)
Date solved : Tuesday, September 30, 2025 at 06:00:57 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

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

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

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

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

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

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

\begin{align*} y(x)&\to \frac {c_1}{x}+c_2 x+c_3 x \log (x) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 15

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

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