Internal problem ID [12097]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 28, Distinct real eigenvalues. Exercises page 282
Problem number: 28.2 (i).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=8 x \left (t \right )+14 y \left (t \right )\\ y^{\prime }\left (t \right )&=7 x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve([diff(x(t),t)=8*x(t)+14*y(t),diff(y(t),t)=7*x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-6 t} c_{1} +c_{2} {\mathrm e}^{15 t} \\ y \left (t \right ) &= -{\mathrm e}^{-6 t} c_{1} +\frac {c_{2} {\mathrm e}^{15 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 71
DSolve[{x'[t]==8*x[t]+14*y[t],y'[t]==7*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-6 t} \left (c_1 \left (2 e^{21 t}+1\right )+2 c_2 \left (e^{21 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-6 t} \left (c_1 \left (e^{21 t}-1\right )+c_2 \left (e^{21 t}+2\right )\right ) \\ \end{align*}