61.2.47 problem Problem 18(L)

Internal problem ID [15285]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 18(L)
Date solved : Thursday, October 02, 2025 at 10:10:03 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

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

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

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 23

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

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

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x*(-x*log(x)*Derivative(y(x), (x, 2)) + 1) + y(x))/(2*x) cannot be solved by the factorable group method