Internal problem ID [14317]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _dAlembert]
\[ \boxed {-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (t \right ) = \operatorname {LambertW}\left (\frac {-c_{1} t +1}{c_{1} t}\right ) t \]
✓ Solution by Mathematica
Time used: 34.75 (sec). Leaf size: 18
DSolve[(-t^(-2)*y[t]^2*Exp[y[t]/t]+1 )+Exp[y[t]/t]*(1+y[t]/t )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t W\left (-1+\frac {e^{c_1}}{t}\right ) \]