Internal problem ID [6515]
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 }\left (t \right )&=x \left (t \right )+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )+y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 5, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ x \left (t \right ) = 2 \,{\mathrm e}^{-2 t}+3 \,{\mathrm e}^{4 t} \] \[ y \left (t \right ) = -2 \,{\mathrm e}^{-2 t}+3 \,{\mathrm e}^{4 t} \]
✓ Solution by Mathematica
Time used: 0.004 (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*}