Internal problem ID [5991]
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: 19.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=3 x \relax (t )-y \relax (t )\\ y^{\prime }\relax (t )&=9 x \relax (t )-3 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.068 (sec). Leaf size: 24
dsolve([diff(x(t),t)=3*x(t)-y(t),diff(y(t),t)=9*x(t)-3*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {1}{9} c_{1}+\frac {1}{3} t c_{1}+\frac {1}{3} c_{2} \] \[ y \relax (t ) = t c_{1}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 34
DSolve[{x'[t]==3*x[t]-y[t],y'[t]==9*x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 3 c_1 t-c_2 t+c_1 \\ y(t)\to 9 c_1 t-3 c_2 t+c_2 \\ \end{align*}