Internal problem ID [6712]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.1. Page 332
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-7 y\\ y^{\prime }&=5 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 78
dsolve([diff(x(t),t)=4*x(t)-7*y(t),diff(y(t),t)=5*x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {{\mathrm e}^{2 t} \left (\sqrt {31}\, \sin \left (\sqrt {31}\, t \right ) c_{2} -\sqrt {31}\, \cos \left (\sqrt {31}\, t \right ) c_{1} -2 \sin \left (\sqrt {31}\, t \right ) c_{1} -2 \cos \left (\sqrt {31}\, t \right ) c_{2} \right )}{5} \\ y \left (t \right ) &= {\mathrm e}^{2 t} \left (\sin \left (\sqrt {31}\, t \right ) c_{1} +\cos \left (\sqrt {31}\, t \right ) c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 98
DSolve[{x'[t]==4*x[t]-7*y[t],y'[t]==5*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{2 t} \cos \left (\sqrt {31} t\right )+\frac {(2 c_1-7 c_2) e^{2 t} \sin \left (\sqrt {31} t\right )}{\sqrt {31}} \\ y(t)\to c_2 e^{2 t} \cos \left (\sqrt {31} t\right )+\frac {(5 c_1-2 c_2) e^{2 t} \sin \left (\sqrt {31} t\right )}{\sqrt {31}} \\ \end{align*}