74.8.27 problem 27

Internal problem ID [16163]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 08:53:16 AM
CAS classification : [[_homogeneous, `class D`], _Bernoulli]

\begin{align*} y-y^{\prime } t&=2 y^{2} \ln \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

\[ y = \frac {t}{2 t \ln \left (t \right )-2 t +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 25

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

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