No chatgpt will upvotePlz 5(a) Find the general solution of the system of equations I'=( 31 ) 1.I.(b) Draw the phase plane and plot several trajectories of the system.

Answered: 5 (a) Find the general solution of the…

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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5. Okay, time for some mathematics. We're going to focus on the interactions between the hares and their main predators, the lynx. The tool we need is differential equations (last seen when we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t, and L(t) the density of lynx at time t. Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares lead to more hares and faster growth. This gives us the differential equation (trust me): HP = aH dt where a is a positive constant. Second we assume that, if there are no hares around, the lynx starve and thus their numbers decay exponentially. This gives us: TP = -bL dt
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Write ÿ – 2ij + 5ý + Y = e', as an autonomous system of first-order equations.
Find the general solution to the system of equations

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5 (a) Find the general solution of the system of equations I' = ( 31 ) 1. I. (b) Draw the phase plane and plot several trajectories of the system.