38.5.26 problem 26

Internal problem ID [8374]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 26
Date solved : Tuesday, September 30, 2025 at 05:32:56 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+2 y&=1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {5}{2}} \\ \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 12

ode:=diff(y(t),t)+2*y(t) = 1; 
ic:=[y(0) = 5/2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 16

ode=D[y[t],t]+2*y[t]==1; 
ic={y[0]==5/2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.074 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) + Derivative(y(t), t) - 1,0) 
ics = {y(0): 5/2} 
dsolve(ode,func=y(t),ics=ics)
 

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