74.8.3 problem 3

Internal problem ID [16068]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 3
Date solved : Monday, March 31, 2025 at 02:38:35 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (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: 0.253 (sec). Leaf size: 41

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

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] (K[1]+1)}dK[1]\&\right ][\log (t)+c_1] \\ y(t)\to -1 \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.255 (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)
 

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