87.13.35 problem 39

Internal problem ID [23518]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 39
Date solved : Thursday, October 02, 2025 at 09:42:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x -1}+\frac {4 y}{\left (x -1\right )^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)+5/(x-1)*diff(y(x),x)+4/(x-1)^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 22

ode=D[y[x],{x,2}]+5/(x-1)*D[y[x],x]+4/(x-1)^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 c_2 \log (x-1)+c_1}{(x-1)^2} \end{align*}

✓ Sympy. Time used: 0.165 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + 5*Derivative(y(x), x)/(x - 1) + 4*y(x)/(x - 1)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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