Internal problem ID [11018]
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(e).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 70
dsolve([diff(x(t),t)-3*x(t)+2*y(t)=0,diff(y(t),t)-x(t)+3*y(t)=0],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = c_{1} \sqrt {7}\, {\mathrm e}^{\sqrt {7}\, t}-c_{2} \sqrt {7}\, {\mathrm e}^{-\sqrt {7}\, t}+3 c_{1} {\mathrm e}^{\sqrt {7}\, t}+3 c_{2} {\mathrm e}^{-\sqrt {7}\, t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{\sqrt {7}\, t}+c_{2} {\mathrm e}^{-\sqrt {7}\, t} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 76
DSolve[{x'[t]-3*x[t]+2*y[t]==0,y'[t]-x[t]+3*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cosh \left (\sqrt {7} t\right )+\frac {(3 c_1-2 c_2) \sinh \left (\sqrt {7} t\right )}{\sqrt {7}} \\ y(t)\to c_2 \cosh \left (\sqrt {7} t\right )+\frac {(c_1-3 c_2) \sinh \left (\sqrt {7} t\right )}{\sqrt {7}} \\ \end{align*}