Consider the system of equationsdx12t°x1 + 7e-2tx2 + cos(t)dt%3Ddx2 =1t?x1 + 6e 2tx2 + sin(t)dt%3DWrite the system in the form: x' =P(t)x+f(t) wherea) x =X1X2b) P(t) =c) f(t) =

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Answered: Consider the system of equations dx1 =…

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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Solve: y" + 4y = 8csc2x O y = C1cos2x + C2 sin2x + 4xcos2x – 2sin2xln(sin2x) %3D O y = C1cos2x + C2 sin2x + 4xcos2x + 2sin2xln(sin2x) y = C1cos2x + C2 sin2x + 2cos2xln(cos2x) + 4xsin2x O y = C1cos2x + C2 sin2x 4xcos2x + 2sin2aln(sin2x) | O y = C1cos2x + C2 sin2x 4xcos2x – 2sin2aln(sin2x) O y = C1cos2x + C2 sin2x 2cos2xln(cos2x) – 4xsin2x |- O y = C1 cos2x + C2 sin2x – 2cos2xln(cos2x) + 4xsin2a O y = C1cos2x + C2 sin2x + 2cos2xln(cos2x) – 4xsin2x
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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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Consider the system of equations dx1 = 2t°x1 + 7e-2tx2 + cos(t) dt dx2 1t?x1 + 6e-2x2 + sin(t) dt %3D P(t)x+f(t) where Write the system in the form: x' = а) х %3 X1 X2 b) P(t) = c) f(t) =