74.7.12 problem 12

Internal problem ID [16089]
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 : 12
Date solved : Tuesday, January 28, 2025 at 08:39:09 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 33

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

\[ y = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \left (\ln \left (\frac {1}{\textit {\_a}}\right ) \textit {\_a} +\ln \left (\frac {1}{\textit {\_a}}\right )+1\right )}d \textit {\_a} +\ln \left (t \right )+c_{1} \right ) t \]

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 39

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

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {1}{K[1] (K[1] \log (K[1])+\log (K[1])-1)}dK[1]=\log (t)+c_1,y(t)\right ] \]