68.5.5 problem 5

Internal problem ID [17256]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 5
Date solved : Thursday, October 02, 2025 at 02:00:01 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} -y+y^{\prime }&=4 t \,{\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(y(t),t)-y(t) = 4*t*exp(-t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{2 t}-2 t -1\right ) {\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 29

ode=D[y[t],t]-y[t]==4*t*Exp[-t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t \left (\int _1^t4 e^{-2 K[1]} K[1]dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*t*exp(-t) - y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{t} + \left (- 2 t - 1\right ) e^{- t} \]