68.5.26 problem 26

Internal problem ID [17277]
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 : 26
Date solved : Thursday, October 02, 2025 at 02:00:41 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} -y+y^{\prime }&=4 \,{\mathrm e}^{t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 11

ode:=diff(y(t),t)-y(t) = 4*exp(t); 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 4 \left (t +1\right ) {\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 13

ode=D[y[t],t]-y[t]==4*Exp[t]; 
ic={y[0]==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 4 e^t (t+1) \end{align*}

✓ Sympy. Time used: 0.074 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) - 4*exp(t) + Derivative(y(t), t),0) 
ics = {y(0): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (4 t + 4\right ) e^{t} \]