Internal problem ID [11767]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 26, Explicit solutions of coupled linear systems. Exercises page 257
Problem number: 26.1 (vii).
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*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x(t),t) = 8*x(t)+14*y(t), diff(y(t),t) = 7*x(t)+y(t), x(0) = 1, y(0) = 1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {4 \,{\mathrm e}^{15 t}}{3}-\frac {{\mathrm e}^{-6 t}}{3} \] \[ y \left (t \right ) = \frac {2 \,{\mathrm e}^{15 t}}{3}+\frac {{\mathrm e}^{-6 t}}{3} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 44
DSolve[{x'[t]==8*x[t]+14*y[t],y'[t]==7*x[t]+y[t]},{x[0]==1,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-6 t} \left (4 e^{21 t}-1\right ) y(t)\to \frac {1}{3} e^{-6 t} \left (2 e^{21 t}+1\right ) \end{align*}