74.7.8 problem 8

Internal problem ID [16006]
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 : 8
Date solved : Thursday, March 13, 2025 at 07:12:22 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.199 (sec). Leaf size: 8

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

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