Internal problem ID [5779]
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(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=5 x \relax (t )+3 y \relax (t )\\ y^{\prime }\relax (t )&=-6 x \relax (t )-4 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 36
dsolve([diff(x(t),t)=5*x(t)+3*y(t),diff(y(t),t)=-6*x(t)-4*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -c_{1} {\mathrm e}^{2 t}-\frac {{\mathrm e}^{-t} c_{2}}{2} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{2 t}+{\mathrm e}^{-t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 61
DSolve[{x'[t]==5*x[t]+3*y[t],y'[t]==-6*x[t]-4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to (2 c_1+c_2) e^{2 t}-(c_1+c_2) e^{-t} \\ y(t)\to 2 (c_1+c_2) e^{-t}-(2 c_1+c_2) e^{2 t} \\ \end{align*}