72.2.3 problem 3

Internal problem ID [14638]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 06:45:49 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

dsolve(diff(y(t),t)=1-2*y(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 24

DSolve[D[y[t],t]==1-2*y[t],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {1}{2}+c_1 e^{-2 t} \\ y(t)\to \frac {1}{2} \\ \end{align*}