64.13.29 problem 29

Internal problem ID [13488]
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 : 29
Date solved : Monday, March 31, 2025 at 07:59:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=(2*x-3)^2*diff(diff(y(x),x),x)-6*(2*x-3)*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 24

ode=(2*x-3)^2*D[y[x],{x,2}]-6*(2*x-3)*D[y[x],x]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 (3-2 x)^3+c_1 (3-2 x) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x - 3)**2*Derivative(y(x), (x, 2)) - (12*x - 18)*Derivative(y(x), x) + 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False