Internal problem ID [11014]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 3(a).
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 )&=3 x \left (t \right )-4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 35
dsolve([diff(x(t),t)=x(t)-2*y(t),diff(y(t),t)=3*x(t)-4*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {2 c_{1} {\mathrm e}^{-2 t}}{3}+{\mathrm e}^{-t} c_{2} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{-2 t}+{\mathrm e}^{-t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 60
DSolve[{x'[t]==x[t]-2*y[t],y'[t]==3*x[t]-4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-2 t} \left (c_1 \left (3 e^t-2\right )-2 c_2 \left (e^t-1\right )\right ) \\ y(t)\to e^{-2 t} \left (3 c_1 \left (e^t-1\right )+c_2 \left (3-2 e^t\right )\right ) \\ \end{align*}