87.3.7 problem 7

Internal problem ID [23256]
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 26
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:27:12 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 24

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

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

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

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

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