Internal problem ID [12558]
Book: Nonlinear Ordinary Differential Equations by D.W.Jordna and P.Smith. 4th edition 1999.
Oxford Univ. Press. NY
Section: Chapter 2. Plane autonomous systems and linearization. Problems page 79
Problem number: 2.1 (iv).
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 )&=2 x \left (t \right )+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 86
dsolve([diff(x(t),t)=x(t)+2*y(t),diff(y(t),t)=2*x(t)+2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\frac {\left (3+\sqrt {17}\right ) t}{2}}+c_{2} {\mathrm e}^{-\frac {\left (-3+\sqrt {17}\right ) t}{2}} \\ y \left (t \right ) &= \frac {c_{1} {\mathrm e}^{\frac {\left (3+\sqrt {17}\right ) t}{2}} \sqrt {17}}{4}-\frac {c_{2} {\mathrm e}^{-\frac {\left (-3+\sqrt {17}\right ) t}{2}} \sqrt {17}}{4}+\frac {c_{1} {\mathrm e}^{\frac {\left (3+\sqrt {17}\right ) t}{2}}}{4}+\frac {c_{2} {\mathrm e}^{-\frac {\left (-3+\sqrt {17}\right ) t}{2}}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 143
DSolve[{x'[t]==x[t]+2*y[t],y'[t]==2*x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{34} e^{-\frac {1}{2} \left (\sqrt {17}-3\right ) t} \left (c_1 \left (-\left (\sqrt {17}-17\right ) e^{\sqrt {17} t}+17+\sqrt {17}\right )+4 \sqrt {17} c_2 \left (e^{\sqrt {17} t}-1\right )\right ) \\ y(t)\to \frac {1}{34} e^{-\frac {1}{2} \left (\sqrt {17}-3\right ) t} \left (4 \sqrt {17} c_1 \left (e^{\sqrt {17} t}-1\right )+c_2 \left (\left (17+\sqrt {17}\right ) e^{\sqrt {17} t}+17-\sqrt {17}\right )\right ) \\ \end{align*}