14.2.13 problem 13 (b)

Internal problem ID [2501]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 13 (b)
Date solved : Sunday, March 30, 2025 at 12:03:53 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {t^{2}}{-t +c_1} \]

✓ Mathematica. Time used: 0.167 (sec). Leaf size: 23

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

\begin{align*} y(t)\to -\frac {t^2}{t-c_1} \\ y(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.197 (sec). Leaf size: 8

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

\[ y{\left (t \right )} = \frac {t^{2}}{C_{1} - t} \]