72.8.21 problem 34

Internal problem ID [14785]
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 : 34
Date solved : Tuesday, January 28, 2025 at 07:15:21 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

dsolve([diff(y(t),t)+5*y(t)= 3*exp(-5*t),y(0) = -2],y(t), singsol=all)
 

\[ y = \left (-2+3 t \right ) {\mathrm e}^{-5 t} \]

✓ Solution by Mathematica

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

DSolve[{D[y[t],t]+5*y[t]== 3*Exp[-5*t],{y[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-5 t} (3 t-2) \]