Internal problem ID [14324]
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: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 18
dsolve([(2*t*y(t)*exp(t^2)+2*t*exp(-y(t)))+(exp(t^2)-t^2*exp(-y(t))+1)*diff(y(t),t)=0,y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {LambertW}\left (-\frac {t^{2}}{{\mathrm e}^{t^{2}}+1}\right ) \]
✓ Solution by Mathematica
Time used: 60.369 (sec). Leaf size: 20
DSolve[{(2*t*y[t]*Exp[t^2]+2*t*Exp[-y[t]])+(Exp[t^2]-t^2*Exp[-y[t]]+1)*y'[t]==0,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to W\left (-\frac {t^2}{e^{t^2}+1}\right ) \]