23.1.188 problem 188

Internal problem ID [4795]
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 : 188
Date solved : Tuesday, September 30, 2025 at 08:40:43 AM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {1}{\ln \left (x \right ) a +c_1 x +a} \]

✓ Mathematica. Time used: 0.112 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {1}{a \log (x)+a+c_1 x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 14

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

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