68.7.36 problem 36

Internal problem ID [17400]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 36
Date solved : Thursday, October 02, 2025 at 02:16:58 PM
CAS classification : [_linear]

\begin{align*} t +y-t y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 10

ode:=t+y(t)-t*diff(y(t),t) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \left (\ln \left (t \right )+1\right ) t \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 11

ode=(t+y[t])-t*D[y[t],t]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t (\log (t)+1) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 8

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

\[ y{\left (t \right )} = t \left (\log {\left (t \right )} + 1\right ) \]