A forest has a population of lynx and a population of rabbits. Let xx represent the number of lynx (in hundreds) above some level, denoted with 0. So x=−3x=-3 corresponds NOT to an absence of lynx, but to a population that is 300 below the designated level of lynx. Similarly, let yy represent the number of rabbits (in hundreds) above a level designated by zero. The following system models the two populations over time:x'=−0.25x+yx′=-0.25x+yy'=−x+4yy′=-x+4ySolve the system using the initial conditions x(0)=0x(0)=0 and y(0)=1y(0)=1.x(t)x(t) = y(t)y(t) = Choose the graph that best represents the solution curve. A forest has a population of lynx and a population of rabbits. Let a represent the number of lynx (inhundreds) above some level, denoted with 0. So x = - 3 corresponds NOT to an absence of lynx, but to apopulation that is 300 below the designated level of lynx. Similarly, let y represent the number of rabbits(in hundreds) above a level designated by zero. The following system models the two populations overtime:x': =0.25x + yy' = - x + 4ySolve the system using the initial conditions (0) = 0 and y(0) = 1.x(t) =y(t) =Choose the graph that best represents the solution curve.O

Solution: x'=dxdt=-0.25x+y .....1y'=dydt=-x+4y .....2B.C.S: x0=0 and y0=1From equation 1 and 2…

Answered: A forest has a population of lynx and a…

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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A forest has a population of lynx and a population of rabbits. Let xx represent the number of lynx (in hundreds) above some level, denoted with 0. So x=−3x=-3 corresponds NOT to an absence of lynx, but to a population that is 300 below the designated level of lynx. Similarly, let yy represent the number of rabbits (in hundreds) above a level designated by zero. The following system models the two populations over time:

x'=−0.25x+yx′=-0.25x+y

y'=−x+4yy′=-x+4y

Solve the system using the initial conditions x(0)=0x(0)=0 and y(0)=1y(0)=1.

x(t)x(t) =

y(t)y(t) =

Choose the graph that best represents the solution curve.