63.5.8 problem 2(b)

Internal problem ID [13003]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 2(b)
Date solved : Wednesday, March 05, 2025 at 08:57:01 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

ode:=diff(y(t),t)+y(t) = exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{t}}{2}+{\mathrm e}^{-t} c_{1} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 21

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

\[ y(t)\to \frac {e^t}{2}+c_1 e^{-t} \]

✓ Sympy. Time used: 0.134 (sec). Leaf size: 12

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

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