Internal problem ID [10776]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x^{\prime }-{\mathrm e}^{\frac {x}{t}}-\frac {x}{t}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(x(t),t)=exp(x(t)/t)+x(t)/t,x(t), singsol=all)
\[ x \left (t \right ) = t \ln \left (-\frac {1}{\ln \left (t \right )+c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.349 (sec). Leaf size: 18
DSolve[x'[t]==Exp[x[t]/t]+x[t]/t,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -t \log (-\log (t)-c_1) \\ \end{align*}