72.3.12 problem 16

Internal problem ID [14676]
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 1.4 page 61
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 06:47:24 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 12

dsolve([diff(y(t),t)=2-y(t),y(0) = 1],y(t), singsol=all)
 

\[ y = 2-{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 14

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

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