74.7.8 problem 8

Internal problem ID [16085]
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
Date solved : Tuesday, January 28, 2025 at 08:38:37 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

\[ y = \frac {t}{-\ln \left (t \right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 21

DSolve[D[y[t],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*}