63.22.3 problem 4(c)

Internal problem ID [13233]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 237
Problem number : 4(c)
Date solved : Tuesday, January 28, 2025 at 05:12:48 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=2 x+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=6 x+3 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 35

dsolve([diff(x(t),t)=2*x(t)+2*y(t),diff(y(t),t)=6*x(t)+3*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{6 t} \\ y &= -\frac {3 \,{\mathrm e}^{-t} c_{1}}{2}+2 c_{2} {\mathrm e}^{6 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 74

DSolve[{D[x[t],t]==2*x[t]+2*y[t],D[y[t],t]==6*x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{7} e^{-t} \left (c_1 \left (3 e^{7 t}+4\right )+2 c_2 \left (e^{7 t}-1\right )\right ) \\ y(t)\to \frac {1}{7} e^{-t} \left (6 c_1 \left (e^{7 t}-1\right )+c_2 \left (4 e^{7 t}+3\right )\right ) \\ \end{align*}