Internal problem ID [14416]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {r^{\prime }-\frac {r^{2}+t^{2}}{r t}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(r(t),t)=(r(t)^2+t^2)/(r(t)*t),r(t), singsol=all)
\begin{align*} r \left (t \right ) &= \sqrt {2 \ln \left (t \right )+c_{1}}\, t \\ r \left (t \right ) &= -\sqrt {2 \ln \left (t \right )+c_{1}}\, t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.177 (sec). Leaf size: 36
DSolve[r'[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*}