Internal problem ID [14925]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number: 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=8 x-y \left (t \right )\\ y^{\prime }\left (t \right )&=x+6 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(x(t),t)=8*x(t)-y(t),diff(y(t),t)=x(t)+6*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{7 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= {\mathrm e}^{7 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 44
DSolve[{x'[t]==8*x[t]-y[t],y'[t]==x[t]+6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{7 t} (c_1 (t+1)-c_2 t) \\ y(t)\to e^{7 t} ((c_1-c_2) t+c_2) \\ \end{align*}