30.5.27 problem 27

Internal problem ID [7526]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 27
Date solved : Tuesday, September 30, 2025 at 04:42:02 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ r = -\frac {3 t^{2}}{t^{3}-3 c_1} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 25

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

\begin{align*} r(t)&\to -\frac {3 t^2}{t^3-3 c_1}\\ r(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 12

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

\[ r{\left (t \right )} = \frac {3 t^{2}}{C_{1} - t^{3}} \]