Internal problem ID [5769]
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(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=5 x \relax (t )+4 y \relax (t )\\ y^{\prime }\relax (t )&=-x \relax (t )+y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 33
dsolve([diff(x(t),t)=5*x(t)+4*y(t),diff(y(t),t)=-x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -{\mathrm e}^{3 t} \left (2 t c_{2}+2 c_{1}+c_{2}\right ) \] \[ y \relax (t ) = {\mathrm e}^{3 t} \left (t c_{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 46
DSolve[{x'[t]==5*x[t]+4*y[t],y'[t]==-x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{3 t} (2 c_1 t+4 c_2 t+c_1) \\ y(t)\to e^{3 t} (c_2-(c_1+2 c_2) t) \\ \end{align*}