74.7.14 problem 14

Internal problem ID [16091]
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 : 14
Date solved : Tuesday, January 28, 2025 at 08:39:25 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} \frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(( 2/t+1/y(t))+(t/y(t)^2)*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = \frac {t}{c_{1} t^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 22

DSolve[( 2/t+1/y[t])+(t/y[t]^2)*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {t}{-1+c_1 t^2} \\ y(t)\to 0 \\ \end{align*}