68.5.59 problem 63 (d)

Internal problem ID [17310]
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 (d)
Date solved : Thursday, October 02, 2025 at 02:01:25 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 6

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

\[ y = \sinh \left (t \right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.077 (sec). Leaf size: 14

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

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