76.2.10 problem 10

Internal problem ID [17267]
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, March 13, 2025 at 09:22:33 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.071 (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]
 

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

✓ Sympy. Time used: 0.250 (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)
 

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