74.6.28 problem 29

Internal problem ID [16051]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 08:31:43 AM
CAS classification : [[_homogeneous, `class A`], _exact, _dAlembert]

\begin{align*} -\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.103 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 31.862 (sec). Leaf size: 18

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

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