I cannot create the correct figure. Please show how to solve and plot the slope field in GEOGEBRA for the system of equations. We will be using purely graphical methods. Consider the system of predator-prey equationsdRdtdFdt=2 (1-B) ₁-16F + 4RFR-RFGenerate a Geogebra figure that shows a plot of a solution curve for this system in the RF-plane,with initial conditions R(0) = 8 and F(0) = 1.

dRdt=21-R3R-RFdFdt=-16F+4RF X=R33dXdt=dRdt∴dXdt=21-X3X-3XFdFdt=-16F+12XFY=F2∴dXdt=21-X3X-6XY…

Answered: Consider the system of predator-prey…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

I cannot create the correct figure. Please show how to solve and plot the slope field in GEOGEBRA for the system of equations. We will be using purely graphical methods.

Consider the system of predator-prey equations
dR
dt
dF
dt
=
2 (1-B) ₁
-16F + 4RF
R-RF
Generate a Geogebra figure that shows a plot of a solution curve for this system in the RF-plane,
with initial conditions R(0) = 8 and F(0) = 1.

Expert Solution

Step 1: Linearizing the system

$\frac{d R}{d t} = 2 (1 - \frac{R}{3}) R - R F \frac{d F}{d t} = - 16 F + 4 R F$

$X = \frac{R}{3} 3 \frac{d X}{d t} = \frac{d R}{d t} ∴ \frac{d X}{d t} = 2 (1 - X) 3 X - 3 X F \frac{d F}{d t} = - 16 F + 12 X F Y = \frac{F}{2} ∴ \frac{d X}{d t} = 2 (1 - X) 3 X - 6 X Y = 6 X (1 - X - Y) \frac{d Y}{d t} = - 32 Y + 24 X Y = 8 Y (3 X - 4)$