Internal problem ID [14024]
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: 38.4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=5 x \left (t \right )-2 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 7, y \left (0\right ) = -7] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve([diff(x(t),t) = x(t)+2*y(t), diff(y(t),t) = 5*x(t)-2*y(t), x(0) = 7, y(0) = -7], singsol=all)
\begin{align*} x \left (t \right ) &= 3 \,{\mathrm e}^{3 t}+4 \,{\mathrm e}^{-4 t} \\ y \left (t \right ) &= 3 \,{\mathrm e}^{3 t}-10 \,{\mathrm e}^{-4 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 44
DSolve[{x'[t]==x[t]+2*y[t],y'[t]==5*x[t]-2*y[t]},{x[0]==8,y[0]==-7},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {2}{7} e^{-4 t} \left (13 e^{7 t}+15\right ) \\ y(t)\to \frac {1}{7} e^{-4 t} \left (26 e^{7 t}-75\right ) \\ \end{align*}