Internal problem ID [1684]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 20
dsolve(exp(t/y(t))*(y(t)-t)*diff(y(t),t)+y(t)*(1+exp(t/y(t)))=0,y(t), singsol=all)
\[ y \relax (t ) = -\frac {t}{\LambertW \left (\frac {c_{1} t}{t c_{1}-1}\right )} \]
✓ Solution by Mathematica
Time used: 1.526 (sec). Leaf size: 34
DSolve[Exp[t/y[t]]*(y[t]-t)*y'[t]+y[t]*(1+Exp[t/y[t]])==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {t}{\text {ProductLog}\left (\frac {t}{t-e^{c_1}}\right )} \\ y(t)\to -e^{\text {ProductLog}(1)} t \\ \end{align*}