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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Q1) Solve the following system of linear equations: [ 3x-2y=2 -z 02) Find the largest possible area of a rectangle that be found in a circle whose diameter is (4). x +y +z = 6 J. 2x-z-5 =-3y n/12 1) Q3) Fi P(3.4 1) P, (23. 2) -sinx R- L- dx
Consider the system Find a particular solution of the form 1(t) = help (formulas) 22(t) = help (formulas) [] = cos(2t) [x2(t)]
please solve it on paper
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
Solve the system dx dt -6 -2 B 20 6 with x (0) x2 = X 2 [B] .]. -2 Give your solution in real form. x1 = An ellipse with counterclockwise orientation " 1. Describe the trajectory.
Write the system of equations in the image in matrix form
TH || Solve the system -4 -2 with 7 (0) 10 4 18 -2 -[:] 1 Give your solution in real form. x₁ (t) = (cos(-2t)+sin(8t)-sin(-2t))e^(2t) x₂(t) = An ellipse with counterclockwise orientation 1. Describe the trajectory.
Write the given linear system in matrix form. Assume X = X' = -7 3 dx dt dy dt dz dt = -7x + 8y - 9z = 3x - y = 10x + 8y + 7z 8 -9 0 -(:)) X + 0.00
5e- 2e- |-7e-/ X = Find dX/dt of Matrix:
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
Solve for the general solution by using separation of variables

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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) =