Internal problem ID [10749]
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: 0.031 (sec). Leaf size: 36
dsolve([diff(x(t),t)=8*x(t)+14*y(t),diff(y(t),t)=7*x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = 2 c_{1} {\mathrm e}^{15 t}-c_{2} {\mathrm e}^{-6 t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{15 t}+c_{2} {\mathrm e}^{-6 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 65
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 (2 (c_1+c_2) e^{21 t}+c_1-2 c_2\right ) \\ y(t)\to \frac {1}{3} e^{-6 t} \left ((c_1+c_2) e^{21 t}-c_1+2 c_2\right ) \\ \end{align*}