78.11.7 problem 7 (a)

Internal problem ID [18207]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 16. The Use of a Known Solution to find Another. Problems at page 121
Problem number : 7 (a)
Date solved : Monday, March 31, 2025 at 05:22:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

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

\[ y = c_1 x +c_2 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 17

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

\[ y(x)\to c_1 e^x-c_2 x \]

✗ Sympy

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

False