74.8.14 problem 14

Internal problem ID [16150]
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 : Tuesday, January 28, 2025 at 08:52:18 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 28

dsolve(diff(r(t),t)=(r(t)^2+t^2)/(r(t)*t),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*}

✓ Solution by Mathematica

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

DSolve[D[r[t],t]==(r[t]^2+t^2)/(r[t]*t),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*}