87.4.18 problem 29

Internal problem ID [23284]
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 37
Problem number : 29
Date solved : Thursday, October 02, 2025 at 09:28:33 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

\[ y = -\frac {3 \sqrt {\ln \left (x \right )}}{2 \ln \left (x \right )^{{3}/{2}}-3 c_1} \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {3 \sqrt {\log (x)}}{-2 \log ^{\frac {3}{2}}(x)+3 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.293 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {3 \sqrt {\log {\left (x \right )}}}{C_{1} - 2 \log {\left (x \right )}^{\frac {3}{2}}} \]