Internal problem ID [5778]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 10. Systems of First-Order Equations. Section A. Drill exercises. Page
400
Problem number: 2(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-3 x \relax (t )+\sqrt {2}\, y \relax (t )\\ y^{\prime }\relax (t )&=\sqrt {2}\, x \relax (t )-2 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 40
dsolve([diff(x(t),t)=-3*x(t)+sqrt(2)*y(t),diff(y(t),t)=sqrt(2)*x(t)-2*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {\left (c_{1} {\mathrm e}^{-t}-2 c_{2} {\mathrm e}^{-4 t}\right ) \sqrt {2}}{2} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{-t}+c_{2} {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 79
DSolve[{x'[t]==-3*x[t]+Sqrt[2]*y[t],y'[t]==Sqrt[2]*x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-4 t} \left (c_1 \left (e^{3 t}+2\right )+\sqrt {2} c_2 \left (e^{3 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-4 t} \left (\sqrt {2} c_1 \left (e^{3 t}-1\right )+2 c_2 e^{3 t}+c_2\right ) \\ \end{align*}