63.23.5 problem 7

Internal problem ID [13245]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 244
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 05:12:58 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=x-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x+7 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 32

dsolve([diff(x(t),t)=x(t)-3*y(t),diff(y(t),t)=3*x(t)+7*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{4 t} \left (c_{2} t +c_{1} \right ) \\ y &= -\frac {{\mathrm e}^{4 t} \left (3 c_{2} t +3 c_{1} +c_{2} \right )}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 46

DSolve[{D[x[t],t]==x[t]-3*y[t],D[y[t],t]==3*x[t]+7*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -e^{4 t} (c_1 (3 t-1)+3 c_2 t) \\ y(t)\to e^{4 t} (3 (c_1+c_2) t+c_2) \\ \end{align*}