74.7.30 problem 30

Internal problem ID [16107]
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 : 30
Date solved : Tuesday, January 28, 2025 at 08:41:35 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 60.154 (sec). Leaf size: 19

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

\[ y(t)\to t \left (1+W\left (\frac {\log (t)+c_1}{e}\right )\right ) \]