Internal problem ID [5993]
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 }\relax (t )&=-x \relax (t )+3 y \relax (t )\\ y^{\prime }\relax (t )&=-3 x \relax (t )+5 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.11 (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)
\[ x \relax (t ) = \frac {{\mathrm e}^{2 t} \left (3 t c_{2}+3 c_{1}-c_{2}\right )}{3} \] \[ y \relax (t ) = {\mathrm e}^{2 t} \left (t c_{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (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_2-c_1) t+c_2) \\ \end{align*}