Internal problem ID [11537]
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 }&=x+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve([diff(x(t),t)=x(t)+2*y(t),diff(y(t),t)=x(t)],singsol=all)
\begin{align*} 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} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 71
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 (c_1 \left (2 e^{3 t}+1\right )+2 c_2 \left (e^{3 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-t} \left (c_1 \left (e^{3 t}-1\right )+c_2 \left (e^{3 t}+2\right )\right ) \\ \end{align*}