14.3.2 problem 4

Internal problem ID [2511]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.9. Exact equations. Excercises page 66
Problem number : 4
Date solved : Sunday, March 30, 2025 at 12:06:00 AM
CAS classification : [_exact]

\begin{align*} 1+\left (1+t y\right ) {\mathrm e}^{t y}+\left (1+t^{2} {\mathrm e}^{t y}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 32

ode:=1+(1+t*y(t))*exp(t*y(t))+(1+t^2*exp(t*y(t)))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {-c_1 t -t^{2}-\operatorname {LambertW}\left (t^{2} {\mathrm e}^{-t \left (c_1 +t \right )}\right )}{t} \]

✓ Mathematica. Time used: 3.173 (sec). Leaf size: 31

ode=(1+(1+t*y[t])*Exp[t*y[t]])+(1+t^2*Exp[t*y[t]])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {W\left (t^2 e^{t (-t+c_1)}\right )}{t}-t+c_1 \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t*y(t) + 1)*exp(t*y(t)) + (t**2*exp(t*y(t)) + 1)*Derivative(y(t), t) + 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out