63.19.6 problem 1(f)

Internal problem ID [13220]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 202
Problem number : 1(f)
Date solved : Tuesday, January 28, 2025 at 05:12:36 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=-6 y \left (t \right )\\ y^{\prime }\left (t \right )&=6 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 22

dsolve([diff(x(t),t)=-6*y(t),diff(y(t),t)=6*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= -c_{2} {\mathrm e}^{6 t}+c_{1} \\ y &= c_{2} {\mathrm e}^{6 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[{D[x[t],t]==-6*y[t],D[y[t],t]==6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -c_2 e^{6 t}+c_1+c_2 \\ y(t)\to c_2 e^{6 t} \\ \end{align*}