87.4.26 problem 41

Internal problem ID [23292]
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 : 41
Date solved : Thursday, October 02, 2025 at 09:28:51 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Riccati]

\begin{align*} y^{\prime }&=\left (1-y\right ) \left (\frac {1}{t}-\frac {1}{10}+\frac {y}{10}\right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=diff(y(t),t) = (1-y(t))*(1/t-1/10+1/10*y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\ln \left (t \right ) t -10 c_1 t +10}{t \left (\ln \left (t \right )-10 c_1 \right )} \]

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 26

ode=D[y[t],t]==(1-y[t])*( (1/t-1/10) +1/10*y[t]) ; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 1+\frac {10}{t \log (t)+10 c_1 t}\\ y(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.287 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-(1 - y(t))*(y(t)/10 - 1/10 + 1/t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 80 t + 1 \]