90.3.23 problem 23

Internal problem ID [25087]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 41
Problem number : 23
Date solved : Thursday, October 02, 2025 at 11:49:46 PM
CAS classification : [_separable]

\begin{align*} \left (1-t \right ) y^{\prime }&=y^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.103 (sec). Leaf size: 23

ode=(1-t)*D[y[t],{t,1}] ==y[t]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{\log (1-t)-c_1}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((1 - t)*Derivative(y(t), t) - y(t)**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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