Internal problem ID [14025]
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: 38.5.
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*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 9] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x(t),t) = 5*x(t)+4*y(t), diff(y(t),t) = 8*x(t)+y(t), x(0) = 0, y(0) = 9], singsol=all)
\begin{align*} x \left (t \right ) &= -3 \,{\mathrm e}^{-3 t}+3 \,{\mathrm e}^{9 t} \\ y \left (t \right ) &= 6 \,{\mathrm e}^{-3 t}+3 \,{\mathrm e}^{9 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
DSolve[{x'[t]==5*x[t]+4*y[t],y'[t]==8*x[t]+y[t]},{x[0]==0,y[0]==9},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 3 e^{-3 t} \left (e^{12 t}-1\right ) \\ y(t)\to 3 e^{-3 t} \left (e^{12 t}+2\right ) \\ \end{align*}