Internal problem ID [14105]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 83.
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 )&=2 x \left (t \right )+2 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 4, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve([diff(x(t),t) = -5*x(t)+4*y(t), diff(y(t),t) = 2*x(t)+2*y(t), x(0) = 4, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= \frac {4 \,{\mathrm e}^{3 t}}{9}+\frac {32 \,{\mathrm e}^{-6 t}}{9} \\ y \left (t \right ) &= \frac {8 \,{\mathrm e}^{3 t}}{9}-\frac {8 \,{\mathrm e}^{-6 t}}{9} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 40
DSolve[{x'[t]==-5*x[t]+4*y[t],y'[t]==2*x[t]+2*y[t]},{x[0]==4,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {4}{9} e^{-6 t} \left (e^{9 t}+8\right ) \\ y(t)\to \frac {8}{9} e^{-6 t} \left (e^{9 t}-1\right ) \\ \end{align*}