68.7.9 problem 9

Internal problem ID [17373]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 9
Date solved : Thursday, October 02, 2025 at 02:14:42 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = \frac {t}{-t +c_1} \]

✓ Mathematica. Time used: 0.151 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.162 (sec). Leaf size: 15

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

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