70.2.10 problem 10

Internal problem ID [18633]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 10
Date solved : Thursday, October 02, 2025 at 03:17:43 PM
CAS classification : [_linear]

\begin{align*} -y+t y^{\prime }&=t^{3} {\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=t*diff(y(t),t)-y(t) = t^3*exp(-t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 26

ode=t*D[y[t],t]-y[t]==t^3*Exp[-t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.151 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**3*exp(-t) + t*Derivative(y(t), t) - y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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