Consider the following system of equations that model the strange dynamics between the two populations of Planet Math: x(t) denotes the population of the mathvillagers and y(t) denotes the population of the biocitizens; t is in years. d = y³ −0.5x² dt dt = y²x³ + 2 Let S(t) = (xs(t), ys(t)) be the solution of the system that goes through the point (2, 0.5) at some time to. Which of the following is true? O Immediately after to, both populations increase. O Immediately after to, the population of mathvillagers to decrease and that of the biocitizens to increase. O Immediately after to, the population of biocitizens to decrease and that of the mathvillager to increase. O Immediately after to, both populations increase.
Consider the following system of equations that model the strange dynamics between the two populations of Planet Math: x(t) denotes the population of the mathvillagers and y(t) denotes the population of the biocitizens; t is in years. d = y³ −0.5x² dt dt = y²x³ + 2 Let S(t) = (xs(t), ys(t)) be the solution of the system that goes through the point (2, 0.5) at some time to. Which of the following is true? O Immediately after to, both populations increase. O Immediately after to, the population of mathvillagers to decrease and that of the biocitizens to increase. O Immediately after to, the population of biocitizens to decrease and that of the mathvillager to increase. O Immediately after to, both populations increase.
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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Should I take the dy/dx of both first or divide them first? Please explain the answer alongside the steps. Thank you!
Transcribed Image Text:Consider the following system of equations that model the strange dynamics between the two populations of
Planet Math: x(t) denotes the population of the mathvillagers and y(t) denotes the population of the biocitizens; t
is in years.
dt
dy
dt
=
= y³ −0.5x²
=y²x³ + 2
Let S(t) = (xs(t), ys (t)) be the solution of the system that goes through the point (2, 0.5) at some time to.
Which of the following is true?
-
O Immediately after to, both populations increase.
O Immediately after to, the population of mathvillagers to decrease and that of the biocitizens to increase.
O Immediately after to, the population of biocitizens to decrease and that of the mathvillager to increase.
O Immediately after to, both populations increase.
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