Internal problem ID [14351]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {y}{t}-\frac {y^{2}}{t^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(t),t)-1/t*y(t)=y(t)^2/t^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {t}{-\ln \left (t \right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 21
DSolve[y'[t]-1/t*y[t]==y[t]^2/t^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t}{-\log (t)+c_1} \\ y(t)\to 0 \\ \end{align*}