Internal problem ID [5776]
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 A. Drill exercises. Page
400
Problem number: 2(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 )&=4 x \relax (t )-7 y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 32
dsolve([diff(x(t),t)=3*x(t)-4*y(t),diff(y(t),t)=4*x(t)-7*y(t)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = \frac {c_{1} {\mathrm e}^{-5 t}}{2}+2 c_{2} {\mathrm e}^{t} \] \[ y \relax (t ) = c_{1} {\mathrm e}^{-5 t}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 73
DSolve[{x'[t]==3*x[t]-4*y[t],y'[t]==4*x[t]-7*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-5 t} \left (c_1 \left (4 e^{6 t}-1\right )-2 c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-5 t} \left (2 c_1 \left (e^{6 t}-1\right )-c_2 \left (e^{6 t}-4\right )\right ) \\ \end{align*}