Internal problem ID [10539]
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 }\left (t \right )&=2 x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=6 x \left (t \right )+3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (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)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {2 \,{\mathrm e}^{-t} c_{1}}{3}+\frac {c_{2} {\mathrm e}^{6 t}}{2} \] \[ y \left (t \right ) = {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{6 t} \]
✓ Solution by Mathematica
Time used: 0.006 (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*}