72.8.7 problem 20

Internal problem ID [14771]
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. Review Exercises for chapter 1. page 136
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 07:14:53 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(t),t)= y(t)+exp(-t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 21

DSolve[D[y[t],t]==y[t]+Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {e^{-t}}{2}+c_1 e^t \]