Internal problem ID [5767]
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(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=-3 x \relax (t )+4 y \relax (t )\\ y^{\prime }\relax (t )&=-2 x \relax (t )+3 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.056 (sec). Leaf size: 31
dsolve([diff(x(t),t)=-3*x(t)+4*y(t),diff(y(t),t)=-2*x(t)+3*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = 2 \,{\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{t} \] \[ y \relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 43
DSolve[{x'[t]==-3*x[t]+4*y[t],y'[t]==-2*x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cosh (t)+(4 c_2-3 c_1) \sinh (t) \\ y(t)\to c_2 (3 \sinh (t)+\cosh (t))-2 c_1 \sinh (t) \\ \end{align*}