Internal problem ID [11557]
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).
ODE order: 1.
ODE degree: 1.
Solve \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: 0.015 (sec). Leaf size: 36
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}^{6 t} c_{1} +c_{2} {\mathrm e}^{-t} \\ y \left (t \right ) &= 2 \,{\mathrm e}^{6 t} c_{1} -\frac {3 c_{2} {\mathrm e}^{-t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 74
DSolve[{x'[t]==2*x[t]+2*y[t],y'[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*}