Internal problem ID [5762]
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 10.2 Linear Systems. Page
380
Problem number: 2(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=x \relax (t )+3 y \relax (t )\\ y^{\prime }\relax (t )&=3 x \relax (t )+y \relax (t ) \end {align*}
With initial conditions \[ [x \relax (0) = 5, y \relax (0) = 1] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x(t),t) = x(t)+3*y(t), diff(y(t),t) = 3*x(t)+y(t), x(0) = 5, y(0) = 1],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = 3 \,{\mathrm e}^{4 t}+2 \,{\mathrm e}^{-2 t} \] \[ y \relax (t ) = 3 \,{\mathrm e}^{4 t}-2 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 38
DSolve[{x'[t]==x[t]+3*y[t],y'[t]==3*x[t]+y[t]},{x[0]==5,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-2 t} \left (3 e^{6 t}+2\right ) \\ y(t)\to e^{-2 t} \left (3 e^{6 t}-2\right ) \\ \end{align*}