49.12.3 problem 2

Internal problem ID [7676]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 108
Problem number : 2
Date solved : Sunday, March 30, 2025 at 12:18:43 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=(3*x-1)^2*diff(diff(y(x),x),x)+(9*x-3)*diff(y(x),x)-9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {9 \left (x -\frac {1}{3}\right )^{2} c_1 +9 c_2}{9 x -3} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 39

ode=(3*x-1)^2*D[y[x],{x,2}]+(9*x-3)*D[y[x],x]-9*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1 \left (-9 x^2+6 x-2\right )-3 i c_2 x (3 x-2)}{6 x-2} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x - 1)**2*Derivative(y(x), (x, 2)) + (9*x - 3)*Derivative(y(x), x) - 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False