87.1.13 problem 14

Internal problem ID [23225]
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 1. Elementary methods. First order differential equations. Exercise at page 9
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:24:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {y-y^{\prime }}{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ y = {\mathrm e}^{x} \left (c_2 \ln \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to e^x (c_2 \log (x)+c_1) \end{align*}

✗ Sympy

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

False