Internal problem ID [5978]
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: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=10 x \relax (t )-5 y \relax (t )\\ y^{\prime }\relax (t )&=8 x \relax (t )-12 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.055 (sec). Leaf size: 36
dsolve([diff(x(t),t)=10*x(t)-5*y(t),diff(y(t),t)=8*x(t)-12*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {5 c_{1} {\mathrm e}^{8 t}}{2}+\frac {c_{2} {\mathrm e}^{-10 t}}{4} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{8 t}+c_{2} {\mathrm e}^{-10 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 73
DSolve[{x'[t]==10*x[t]-5*y[t],y'[t]==8*x[t]-12*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{9} e^{-t} (9 c_1 \cosh (9 t)+(11 c_1-5 c_2) \sinh (9 t)) \\ y(t)\to \frac {1}{9} e^{-10 t} \left ((4 c_1-c_2) e^{18 t}-4 c_1+10 c_2\right ) \\ \end{align*}