68.5.56 problem 63 (a)

Internal problem ID [17307]
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 : 63 (a)
Date solved : Thursday, October 02, 2025 at 02:01:21 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 11

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

\[ y = t -1+{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.066 (sec). Leaf size: 10

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

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