74.8.14 problem 14

Internal problem ID [16079]
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 : 14
Date solved : Monday, March 31, 2025 at 02:39:11 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 28

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

\begin{align*} r &= \sqrt {2 \ln \left (t \right )+c_1}\, t \\ r &= -\sqrt {2 \ln \left (t \right )+c_1}\, t \\ \end{align*}

✓ Mathematica. Time used: 0.186 (sec). Leaf size: 36

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

\begin{align*} r(t)\to -t \sqrt {2 \log (t)+c_1} \\ r(t)\to t \sqrt {2 \log (t)+c_1} \\ \end{align*}

✓ Sympy. Time used: 0.355 (sec). Leaf size: 29

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

\[ \left [ r{\left (t \right )} = - t \sqrt {C_{1} + 2 \log {\left (t \right )}}, \ r{\left (t \right )} = t \sqrt {C_{1} + 2 \log {\left (t \right )}}\right ] \]