Internal problem ID [5773]
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(g).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=7 x \relax (t )+6 y \relax (t )\\ y^{\prime }\relax (t )&=2 x \relax (t )+6 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.054 (sec). Leaf size: 36
dsolve([diff(x(t),t)=7*x(t)+6*y(t),diff(y(t),t)=2*x(t)+6*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -\frac {3 c_{1} {\mathrm e}^{3 t}}{2}+2 c_{2} {\mathrm e}^{10 t} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{10 t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 74
DSolve[{x'[t]==7*x[t]+6*y[t],y'[t]==2*x[t]+6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{7} e^{3 t} \left (c_1 \left (4 e^{7 t}+3\right )+6 c_2 \left (e^{7 t}-1\right )\right ) \\ y(t)\to \frac {1}{7} e^{3 t} \left (2 c_1 \left (e^{7 t}-1\right )+c_2 \left (3 e^{7 t}+4\right )\right ) \\ \end{align*}