68.5.31 problem 31

Internal problem ID [17282]
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 : 31
Date solved : Thursday, October 02, 2025 at 02:00:49 PM
CAS classification : [_linear]

\begin{align*} t y^{\prime }+y&=2 \,{\mathrm e}^{t} t \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 18

ode:=t*diff(y(t),t)+y(t) = 2*t*exp(t); 
ic:=[y(1) = -1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to \frac {2 e^t (t-1)-1}{t} \end{align*}

✓ Sympy. Time used: 0.143 (sec). Leaf size: 17

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

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