87.4.27 problem 42

Internal problem ID [23293]
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 : 42
Date solved : Thursday, October 02, 2025 at 09:28:53 PM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=\left (1-y\right ) \left (-\frac {1}{t \ln \left (t \right )}-\frac {3}{100}+\frac {3 y}{100}\right ) \end{align*}

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

ode:=diff(y(t),t) = (1-y(t))*(-1/t/ln(t)-3/100+3/100*y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = 1-\frac {2 \ln \left (t \right )}{c_1 -\frac {3 t \ln \left (t \right )}{50}+\frac {3 t}{50}} \]

✓ Mathematica. Time used: 0.143 (sec). Leaf size: 29

ode=D[y[t],t]==(1-y[t])*( (-1/(t*Log[t]) -3/100 ) +3/100*y[t]) ; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 1+\frac {\log (t)}{\frac {3}{100} t (\log (t)-1)+c_1}\\ y(t)&\to 1 \end{align*}

✓ Sympy. Time used: 1.232 (sec). Leaf size: 34

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-(1 - y(t))*(3*y(t)/100 - 3/100 - 1/(t*log(t))) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {100 C_{1} + 3 t \log {\left (t \right )} - 3 t + 100 \log {\left (t \right )}}{100 C_{1} + 3 t \log {\left (t \right )} - 3 t} \]