72.6.2 problem 2

Internal problem ID [14727]
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 1.8 page 121
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 07:12:55 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 15

dsolve(diff(y(t),t)=-4*y(t)+3*exp(-t),y(t), singsol=all)
 

\[ y = \left ({\mathrm e}^{3 t}+c_{1} \right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 19

DSolve[D[y[t],t]==-4*y[t]+3*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (e^{3 t}+c_1\right ) \]