Internal problem ID [14352]
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: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {y}{t}-\frac {y^{2}}{t}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve(diff(y(t),t)-1/t*y(t)=y(t)^2/t,y(t), singsol=all)
\[ y \left (t \right ) = \frac {t}{-t +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.383 (sec). Leaf size: 32
DSolve[y'[t]-1/t*y[t]==y[t]^2/t,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{c_1} t}{1-e^{c_1} t} \\ y(t)\to -1 \\ y(t)\to 0 \\ \end{align*}