Internal problem ID [11561]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 218
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=x-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x-4 y \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 3, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 34
dsolve([diff(x(t),t) = x(t)-2*y(t), diff(y(t),t) = 3*x(t)-4*y(t), x(0) = 3, y(0) = 1],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = 7 \,{\mathrm e}^{-t}-4 \,{\mathrm e}^{-2 t} \] \[ y \left (t \right ) = 7 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 34
DSolve[{x'[t]==x[t]-2*y[t],y'[t]==3*x[t]-4*y[t]},{x[0]==3,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-2 t} \left (7 e^t-4\right ) y(t)\to e^{-2 t} \left (7 e^t-6\right ) \end{align*}