44.5.26 problem 26

Internal problem ID [7088]
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, January 28, 2025 at 08:48:20 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*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

dsolve([diff(y(t),t)+2*y(t)=1,y(0) = 5/2],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 16

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

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