59.3.12 problem Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 3

Internal problem ID [10014]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 3
Date solved : Sunday, March 30, 2025 at 02:53:08 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = \frac {c_1 \left (x -2\right )^{4}+c_2}{x -2} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.234 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} \left (x - 2\right ) \]