Internal problem ID [6746]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.2. Page 346
Problem number: 21.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=-3 x \left (t \right )+5 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 35
dsolve([diff(x(t),t)=-x(t)+3*y(t),diff(y(t),t)=-3*x(t)+5*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{2 t} \left (3 c_{2} t +3 c_{1} -c_{2} \right )}{3} \] \[ y \left (t \right ) = {\mathrm e}^{2 t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 46
DSolve[{x'[t]==-x[t]+3*y[t],y'[t]==-3*x[t]+5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{2 t} (-3 c_1 t+3 c_2 t+c_1) y(t)\to e^{2 t} (-3 c_1 t+3 c_2 t+c_2) \end{align*}