Internal problem ID [14031]
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: 38.10 (e).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-13 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 2, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 35
dsolve([diff(x(t),t) = 4*x(t)-13*y(t), diff(y(t),t) = x(t), x(0) = 2, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{2 t} \left (-3 \sin \left (3 t \right )+2 \cos \left (3 t \right )\right ) \\ y \left (t \right ) &= {\mathrm e}^{2 t} \cos \left (3 t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 37
DSolve[{x'[t]==4*x[t]-13*y[t],y'[t]==x[t]},{x[0]==2,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{2 t} (2 \cos (3 t)-3 \sin (3 t)) \\ y(t)\to e^{2 t} \cos (3 t) \\ \end{align*}