Internal problem ID [10519]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 190
Problem number: 3(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 36
dsolve([diff(x(t),t)=x(t)+2*y(t),diff(y(t),t)=x(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -{\mathrm e}^{-t} c_{1} +2 c_{2} {\mathrm e}^{2 t} \] \[ y \left (t \right ) = {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 65
DSolve[{x'[t]==x[t]+2*y[t],y'[t]==x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-t} \left (2 (c_1+c_2) e^{3 t}+c_1-2 c_2\right ) \\ y(t)\to \frac {1}{3} e^{-t} \left ((c_1+c_2) e^{3 t}-c_1+2 c_2\right ) \\ \end{align*}