Internal problem ID [6532]
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 }\left (t \right )&=5 x \left (t \right )+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=-6 x \left (t \right )-4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{2 t} \\ y \left (t \right ) &= -2 \,{\mathrm e}^{-t} c_{1} -c_{2} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 66
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 e^{-t} \left (c_1 \left (2 e^{3 t}-1\right )+c_2 \left (e^{3 t}-1\right )\right ) \\ y(t)\to e^{-t} \left (-2 c_1 \left (e^{3 t}-1\right )-c_2 \left (e^{3 t}-2\right )\right ) \\ \end{align*}