4 Classify the equilibrium is x = [0,0] for the first order system d x₁(t) 2 a [228] - [ 1 ² ] [ 28 ] = 10 6 (t) (t)

Q: y (4) + y" +y" = 0, where y(0) = y'(0) = y″(0) = 0, y″(0) = 1

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Q: y(t) – S y(t)sen2(t – t)dt = sen2t

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Q: 9. (a) Show that the functions r(t) = 3et+ 7e-t and y(t) = 3et+ 21e are solutions of the system I' =…

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Q: Solve the system dx dt x(0) = x(t) = 10] = with the initial value = -20 16 -24 20 15 [5]. 20

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Q: Help me fast so that I will give Upvote.

A: The Laplace transform of the function f(t) is defined as L[f(t)]=∫0∞e-stf(t)dt, where s>0. Since…

Q: Find the general solution of the given system of equations and then describe how the solutions…

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Q: ) This is the second part of a three-part problem. Consider the system of differential equations…

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Q: Solve the simultaneous ODES (a) x"(t) + 4x(t) + 5y(t) = t²,_y"(t) + 5x(t) + 4y(t) = t +1

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Q: A Bernoulli differential equation is one of the form dy + P(x)y= Q(x)y" (*) da y ¹ Observe that, if…

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Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' +y = 0. If W(y1, Y2)(2) = e² , then W…

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Q: Suppose (t + 2)y (t-6)y E 5ty + 7y2, 5yı + 8tyz, P(t) = a. This system of linear differential…

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Q: (b) -x X x + y y - 4y + 2z = - - (x, y, z) = 10 Z = 2 z = 1

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Q: -S₁ (3 + e-") 5(e-3) dt =

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Suppose (t + 4) y { (t — 6)y/ - = = P(t) a. This system of linear differential equations can be put…

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Q: Write each system in matrix form- = Ax. dx dt Determine the eigenvalues of A. State whether the…

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Q: t with y(0) Solve y + 5y ing %3D 4 express- the particular solution as a convolution.

A: In this question, we have to find the particular solution of the differential equation by help of…

Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x₁…

A: Here we have to find the particular solution of given linear system with given initial conditions.

Q: The result of the convolution; y(t) = 7e-5t y(t) = L-1 {(7/(s+5))*e-S} Ⓒy(t) = L-1 {(7/(s+5)).e-S} =…

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Q: Get all the balance points ii = -x1 + 2x + x2 -x1 - x2 E = {T1,T2} Obtain all the equilibrium points…

A: Equilibrium Points: Let z=f(x,y) is a function of x and y, where x and y are the functions of t,…

Q: 1. Let D = the sales of DVDs in billions of dollars, S = the total sales of streaming videos in…

A: The sales of dvds given as the function D = -0.92t + 8.75 and the total sales of streaming videos…

Q: Find the equilibrium point. D(x) = (x-7), S(x) =x O A. (7,$0) О В. (14,549) C. 2,$12.25 O D. (0,$49)

A: The equilibrium point of two functions D(x) and S(x) is the point which satisfies both equations. In…

Q: Which of the following functions V(y1, y2) is a Lyapunov function for the dynamical system y₁ =…

A: To Find : Which of the following function Vy1 , y2 is Lyapunov function for the dynamic system.…

Q: 2x- (ii) Given aty=b²x-y and a 4x+3 = bx-5y, show that 3y-6x=7x² +5y²

A: (ii) Given ax+y=b2x-y and a4x+3=bx-5y We will use logarithm properties to solve the given:

Q: [2][3][2]+[1]. ] + [ 1 ] e(t), y(t) = [1 − 1] [ 21 (1)] + e(t) (t) (t) d 1(t) dt x2(t) -1 0 For x₁…

A: given :             ddtx1tx2t =-1102x1tx2t +10 etyt=1-1x1tx2t+et To Find : Y(s)

Q: Q(4) Find the general solution of dy =(r- y+ 5). dr

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Q: Consider the second order linear equation with constant coefficients ay" (x) + by (x) + cy(x) = 0…

A: The  given  equation  is                                     Let be   a  trial  solution of the…

Q: Transform the following equations into a system of first order equations. t²u" + tư' + (t2 – 0.25)u…

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Q: F- -(0) = 2, y(0) = – 14 æ(t) = y(t) =

A: We have to solve the given system.                                          x'y'=21-41-8xy with…

Q: . Find the general solution of the third-order ODE y(4) — 5y(³) + 6y″ + 4y′ − 8y = 0, note that m² −…

A: Given the third order ordinary differential equation, y4-5y3+6y''+4y'-8y=0. To find the general…

Q: x(t) = Find real-valued closed formulas for the trajectory (t + 1) = Ax(t), where z (0) = [!] A 9 12…

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: The solution of y" = 8(t – 1) – 6(t – 3), y(0) = y'(0) = 0 is y(t) = %3D (A) (t- 3)[u(t - 1) - u(t-…

A: Given y''=δt-1-δt-3, y0=y'0=0

Q: particle moves along a straight horizontal line so that its position at any time is given by s(t) =…

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Q: b) Solve ди Ət ди +3x = 1+u, Әх -8AHAB, u(x,0) = f(x). t > 0,

A: Given pde is  ∂u∂t+3x∂u∂x=1+u,  -∞<x<∞, t>0 and u(x,0)=f(x) we have to solve this pde

Q: 5. Let h - Ah = x = [1 + ²√5 h = √5], 0 where h is a real parameter. (a) Find all values of h for…

A: The question is from stability analysis.

Q: 7. Find: t2 (a) / V1+ t3 (x2 + 2)(x – 3) dx (b) / * /. - 2.x (c) xV (16 – x4 dx

A: To evaluate.a ∫01 t21+t3 dtb ∫x2+2x-32x  dxc ∫-22 x16-x4 dx

Q: Consider the system of equations x -5 - (2010) * X 20 -10 (a) Use a graphing utility to graph a…

A: x'=10-520-10x

Q: Let 2 A = -3 Find the unique solution to the system X' = AX satisfying the initial condition [2¹].…

A: Let X=xy X'=AXA=-320-3X0=-12x0=-1y0=2X'=AX⇒dxdtdydt=-320-3xy⇒dxdtdydt=-3x+2y-3ydxdt=-3x+2y…