74.7.31 problem 31

Internal problem ID [16108]
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 : 31
Date solved : Tuesday, January 28, 2025 at 08:41:39 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \end{align*}

✓ Solution by Maple

Time used: 0.741 (sec). Leaf size: 31

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

\[ y = t \,{\mathrm e}^{-\operatorname {RootOf}\left (-2 \textit {\_Z} -{\mathrm e}^{{\mathrm e}^{\textit {\_Z}}+\textit {\_Z}}+{\mathrm e}^{{\mathrm e}^{\textit {\_Z}}}+2 \ln \left (t \right )+2 c_{1} \right )} \]

✓ Solution by Mathematica

Time used: 0.262 (sec). Leaf size: 43

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

\[ \text {Solve}\left [\frac {t e^{\frac {t}{y(t)}} \left (\frac {y(t)}{t}-1\right )}{y(t)}+2 \log \left (\frac {y(t)}{t}\right )=-2 \log (t)+c_1,y(t)\right ] \]