23.1.429 problem 419

Internal problem ID [5036]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 419
Date solved : Tuesday, September 30, 2025 at 11:28:22 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.175 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {C_{1}}{\log {\left (x \right )}} + a x \]