Internal problem ID [6013]
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 8.3. Page 354
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=5 x \relax (t )+9 y \relax (t )+2\\ y^{\prime }\relax (t )&=-x \relax (t )+11 y \relax (t )+6 \end {align*}
✓ Solution by Maple
Time used: 0.054 (sec). Leaf size: 38
dsolve([diff(x(t),t)=5*x(t)+9*y(t)+2,diff(y(t),t)=-x(t)+11*y(t)+6],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {1}{2}+{\mathrm e}^{8 t} \left (3 t c_{1}-c_{1}+3 c_{2}\right ) \] \[ y \relax (t ) = -\frac {1}{2}+{\mathrm e}^{8 t} \left (t c_{1}+c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 54
DSolve[{x'[t]==5*x[t]+9*y[t]+2,y'[t]==-x[t]+11*y[t]+6},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2}+e^{8 t} (-3 c_1 t+9 c_2 t+c_1) \\ y(t)\to -\frac {1}{2}+e^{8 t} (c_1 (-t)+3 c_2 t+c_2) \\ \end{align*}