Internal problem ID [14373]
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: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve((t*y(t))*diff(y(t),t)-(t^2*exp(-y(t)/t)+y(t)^2)=0,y(t), singsol=all)
\[ y \left (t \right ) = \left (\operatorname {LambertW}\left (\left (\ln \left (t \right )+c_{1} \right ) {\mathrm e}^{-1}\right )+1\right ) t \]
✓ Solution by Mathematica
Time used: 60.23 (sec). Leaf size: 19
DSolve[(t*y[t])*y'[t]-(t^2*Exp[-y[t]/t]+y[t]^2)==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t \left (1+W\left (\frac {\log (t)+c_1}{e}\right )\right ) \]