Internal problem ID [11549]
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(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-2 x-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x+4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 95
dsolve([diff(x(t),t)=-2*x(t)-3*y(t),diff(y(t),t)=-x(t)+4*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -2 c_{1} {\mathrm e}^{\left (1+2 \sqrt {3}\right ) t} \sqrt {3}+2 c_{2} {\mathrm e}^{-\left (-1+2 \sqrt {3}\right ) t} \sqrt {3}+3 c_{1} {\mathrm e}^{\left (1+2 \sqrt {3}\right ) t}+3 c_{2} {\mathrm e}^{-\left (-1+2 \sqrt {3}\right ) t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{\left (1+2 \sqrt {3}\right ) t}+c_{2} {\mathrm e}^{-\left (-1+2 \sqrt {3}\right ) t} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 144
DSolve[{x'[t]==-2*x[t]-3*y[t],y'[t]==-x[t]+4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {1}{4} e^{t-2 \sqrt {3} t} \left (c_1 \left (\left (\sqrt {3}-2\right ) e^{4 \sqrt {3} t}-2-\sqrt {3}\right )+\sqrt {3} c_2 \left (e^{4 \sqrt {3} t}-1\right )\right ) y(t)\to \frac {1}{12} e^{t-2 \sqrt {3} t} \left (3 c_2 \left (\left (2+\sqrt {3}\right ) e^{4 \sqrt {3} t}+2-\sqrt {3}\right )-\sqrt {3} c_1 \left (e^{4 \sqrt {3} t}-1\right )\right ) \end{align*}