Internal problem ID [5770]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 10. Systems of First-Order Equations. Section 10.3 Homogeneous Linear Systems
with Constant Coefficients. Page 387
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=4 x \relax (t )-3 y \relax (t )\\ y^{\prime }\relax (t )&=8 x \relax (t )-6 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.05 (sec). Leaf size: 27
dsolve([diff(x(t),t)=4*x(t)-3*y(t),diff(y(t),t)=8*x(t)-6*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {{\mathrm e}^{-2 t} c_{2}}{2}+\frac {3 c_{1}}{4} \] \[ y \relax (t ) = c_{1}+{\mathrm e}^{-2 t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 55
DSolve[{x'[t]==4*x[t]-3*y[t],y'[t]==8*x[t]-6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-t} (c_1 \cosh (t)+(5 c_1-3 c_2) \sinh (t)) \\ y(t)\to e^{-t} (8 c_1 \sinh (t)+c_2 (\cosh (t)-5 \sinh (t))) \\ \end{align*}