Internal problem ID [12237]
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 (iii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-4 x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )-2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 83
dsolve([diff(x(t),t)=-4*x(t)+2*y(t),diff(y(t),t)=3*x(t)-2*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {c_{1} {\mathrm e}^{\left (-3+\sqrt {7}\right ) t} \sqrt {7}}{3}-\frac {c_{2} {\mathrm e}^{-\left (3+\sqrt {7}\right ) t} \sqrt {7}}{3}-\frac {c_{1} {\mathrm e}^{\left (-3+\sqrt {7}\right ) t}}{3}-\frac {c_{2} {\mathrm e}^{-\left (3+\sqrt {7}\right ) t}}{3} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{\left (-3+\sqrt {7}\right ) t}+c_{2} {\mathrm e}^{-\left (3+\sqrt {7}\right ) t} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 143
DSolve[{x'[t]==-4*x[t]+2*y[t],y'[t]==3*x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{14} e^{-\left (\left (3+\sqrt {7}\right ) t\right )} \left (c_1 \left (-\left (\sqrt {7}-7\right ) e^{2 \sqrt {7} t}+7+\sqrt {7}\right )+2 \sqrt {7} c_2 \left (e^{2 \sqrt {7} t}-1\right )\right ) y(t)\to \frac {1}{14} e^{-\left (\left (3+\sqrt {7}\right ) t\right )} \left (3 \sqrt {7} c_1 \left (e^{2 \sqrt {7} t}-1\right )+c_2 \left (\left (7+\sqrt {7}\right ) e^{2 \sqrt {7} t}+7-\sqrt {7}\right )\right ) \end{align*}