74.22.3 problem 3

Internal problem ID [16650]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 09:16:14 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 14

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

\begin{align*} x \left (t \right ) &= c_{2} \\ y &= c_{1} {\mathrm e}^{-2 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 28

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

\begin{align*} x(t)\to c_1 \\ y(t)\to c_2 e^{-2 t} \\ x(t)\to c_1 \\ y(t)\to 0 \\ \end{align*}