74.7.9 problem 9

Internal problem ID [16086]
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
Date solved : Tuesday, January 28, 2025 at 08:38:40 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(diff(y(t),t)-1/t*y(t)=y(t)^2/t,y(t), singsol=all)
 

\[ y = \frac {t}{-t +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.246 (sec). Leaf size: 41

DSolve[D[y[t],t]-1/t*y[t]==y[t]^2/t,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] (K[1]+1)}dK[1]\&\right ][\log (t)+c_1] \\ y(t)\to -1 \\ y(t)\to 0 \\ \end{align*}