Internal problem ID [11562]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 218
Problem number: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=5 x-y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x+y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 2, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 34
dsolve([diff(x(t),t) = 5*x(t)-y(t), diff(y(t),t) = 3*x(t)+y(t), x(0) = 2, y(0) = -1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {7 \,{\mathrm e}^{4 t}}{2}-\frac {3 \,{\mathrm e}^{2 t}}{2} \] \[ y \left (t \right ) = \frac {7 \,{\mathrm e}^{4 t}}{2}-\frac {9 \,{\mathrm e}^{2 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 44
DSolve[{x'[t]==5*x[t]-y[t],y'[t]==3*x[t]+y[t]},{x[0]==2,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{2 t} \left (7 e^{2 t}-3\right ) y(t)\to \frac {1}{2} e^{2 t} \left (7 e^{2 t}-9\right ) \end{align*}