90.1.17 problem 28

Internal problem ID [25041]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 28
Date solved : Thursday, October 02, 2025 at 11:47:45 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=t \,{\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(t),t) = t*exp(-t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (-t -1\right ) {\mathrm e}^{-t}+c_1 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 18

ode=D[y[t],{t,1}]== t*Exp[-t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -e^{-t} (t+1)+c_1 \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = C_{1} - t e^{- t} - e^{- t} \]