Internal problem ID [5761]
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(a).
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*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 35
dsolve([diff(x(t),t)=x(t)+3*y(t),diff(y(t),t)=3*x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = c_{1} {\mathrm e}^{4 t}-c_{2} {\mathrm e}^{-2 t} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 46
DSolve[{x'[t]==x[t]+3*y[t],y'[t]==3*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_1 \cosh (3 t)+c_2 \sinh (3 t)) \\ y(t)\to e^t (c_2 \cosh (3 t)+c_1 \sinh (3 t)) \\ \end{align*}