Internal problem ID [1689]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.9. Page 66
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {1+{\mathrm e}^{y t} \left (1+y t \right )+\left (1+{\mathrm e}^{y t} t^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(1+exp(t*y(t))*(1+t*y(t))+(1+exp(t*y(t))*t^2)*diff(y(t),t) = 0,y(t), singsol=all)
\[ y \relax (t ) = -\frac {t c_{1}+t^{2}+\LambertW \left (t^{2} {\mathrm e}^{-t c_{1}} {\mathrm e}^{-t^{2}}\right )}{t} \]
✓ Solution by Mathematica
Time used: 3.045 (sec). Leaf size: 31
DSolve[1+Exp[t*y[t]]*(1+t*y[t])+(1+Exp[t*y[t]]*t^2)*y'[t] == 0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {\text {ProductLog}\left (t^2 e^{t (-t+c_1)}\right )}{t}-t+c_1 \\ \end{align*}