Internal problem ID [13719]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 38. Systems of differential equations. A starting point. Additional Exercises.
page 786
Problem number: 38.11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+4 y \left (t \right )\\ y^{\prime }\left (t \right )&=8 x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve([diff(x(t),t)=5*x(t)+4*y(t),diff(y(t),t)=8*x(t)+y(t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = c_{1} {\mathrm e}^{9 t}-\frac {c_{2} {\mathrm e}^{-3 t}}{2} y \left (t \right ) = c_{1} {\mathrm e}^{9 t}+c_{2} {\mathrm e}^{-3 t} \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 71
DSolve[{x'[t]==5*x[t]+4*y[t],y'[t]==8*x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-3 t} \left (c_1 \left (2 e^{12 t}+1\right )+c_2 \left (e^{12 t}-1\right )\right ) y(t)\to \frac {1}{3} e^{-3 t} \left (2 c_1 \left (e^{12 t}-1\right )+c_2 \left (e^{12 t}+2\right )\right ) \end{align*}