74.7.32 problem 32

Internal problem ID [16109]
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 : 32
Date solved : Tuesday, January 28, 2025 at 08:41:43 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.099 (sec). Leaf size: 14

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

\[ y = \frac {\operatorname {LambertW}\left ({\mathrm e}^{-1} t c_{1} \right )}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 38

DSolve[t*(Log[t]-Log[y[t]] )*D[y[t],t]==y[t],y[t],t,IncludeSingularSolutions -> True]
 

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