Internal problem ID [11555]
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: 3(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-14 \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 77
dsolve([diff(x(t),t)=2*x(t)+3*y(t),diff(y(t),t)=-x(t)-14],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -14+{\mathrm e}^{t} \left (\sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) c_{1} -\sqrt {2}\, \cos \left (\sqrt {2}\, t \right ) c_{2} -\sin \left (\sqrt {2}\, t \right ) c_{2} -\cos \left (\sqrt {2}\, t \right ) c_{1} \right ) \] \[ y \left (t \right ) = \frac {28}{3}+{\mathrm e}^{t} \left (\sin \left (\sqrt {2}\, t \right ) c_{2} +\cos \left (\sqrt {2}\, t \right ) c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.315 (sec). Leaf size: 89
DSolve[{x'[t]==2*x[t]+3*y[t],y'[t]==-x[t]-14},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t \cos \left (\sqrt {2} t\right )+\frac {(c_1+3 c_2) e^t \sin \left (\sqrt {2} t\right )}{\sqrt {2}}-14 y(t)\to c_2 e^t \cos \left (\sqrt {2} t\right )-\frac {(c_1+c_2) e^t \sin \left (\sqrt {2} t\right )}{\sqrt {2}}+\frac {28}{3} \end{align*}