Internal problem ID [10536]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 225
Problem number: 1(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 32
dsolve([diff(x(t),t)=x(t)-y(t),diff(y(t),t)=x(t)+3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -{\mathrm e}^{2 t} \left (t c_{2} +c_{1} -c_{2} \right ) \] \[ y \left (t \right ) = {\mathrm e}^{2 t} \left (t c_{2} +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 42
DSolve[{x'[t]==x[t]-y[t],y'[t]==x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -e^{2 t} (c_1 (t-1)+c_2 t) \\ y(t)\to e^{2 t} ((c_1+c_2) t+c_2) \\ \end{align*}