Consider a system model given by d²x (t) dt² x (0) = 1 dx (t) dt - It=0 What is the free response? O 2t + 1 0 1 1 — =t = 2. -t³+2t+1 6 2t³+3t+1 + 2t

Q: Q2: If D = d dt > find a complete solution of: (D+2)x+ (D+4)y = 1 (D+1)x+ (D+5)y = 2

A:

Q: Note: - You are attempting question 7 out of 12 dx The equilibrium points of the system =( dt a)…

A:

Q: Solve the system dx dt with the initial value -4 [3] -3 x(0) = -11 9 [2:]- -6 4 x(t) = X

A:

Q: GSolve the system 5 -6 dx x dt 10 with the initial value -11 x (0) 18 -3 x(t) =

A:

Q: If f(t) dt 30 x + 183 e + f(t) dt then f(0)%D 218 O 213 O 203 O 220 O 208

A:

Q: A form of a particular solution to = 2x + 3y-7 dt = -x - 2y +5 is dt O (a b)" O (7, 5)" O (2, y)" O…

A:

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

A:

Q: 0<t<n Find b, if f(t) = %3D A n<t<2n a) bn= 0 O d) bn= 3t/2n O b) bn= 4A/(nn ) O c) bn= r/2n O

A: Here, given function f(t) is an even function.

Q: Let a system be given by dx = (a – x) x² dt where a is a real number. (3.1) How should a be chosen…

A: Given: The system is defined as If a = 0, then

Q: + x + + 3y where x(0) = 0 and y(0) = 0. ||||

A:

Q: 1. d²y dt2 dy + 6- +8y=2e-3t dt 2. d²y dy +4 dt² dt +13y = e-t 3. d²y dy +7 +10y=e-2t dt2 dt

A:

Q: 3t+4 dt 1 (t+1)(t+2) 2.

A:

Q: Suppose that the damping effect of the system is changed (b-10). How will this affect the response…

A: As per the question we are given a mass-spring-damping system as : mass m = 1 spring constant k = 6…

Q: Consider a system model given by d²x(1) dx (1) d1² + dt =1. What is the particular solution? Ox_(t)…

A: The system model is given by,Let,Thus, above equation becomes,

Q: Q4: Solve the system of ODE's: (2D+3)x+ (D+4)y = -Cost (D+1)x+ (D + 2)y= 2 Sint where D=d/dt

A:

Q: Solve the system dx 4x %3D dt dy 3y + z dt dz -y + z dt

A:

Q: (1 point) Solve the system 1 6 dx dt -1 6 with the initial value 13 æ(0) = 6 a(t) = %3D

A:

Q: dt d Ət u(t) = 6 u(t) + 2 v(t) v(t) = 2 v(t) — 7 u(t)

A:

Q: D = d/dt, Solve dx/dt + 2x – 3y = 5t dy/dt - 3x + 2y = 2e2t

A: given dxdt+2x-3y=5t⇒D+2x-3y=5t   ...idydt-3x+2y=2e2t⇒-3x+D+2y=2e2t   ...ii multiply equation (i) by…

Q: 1. Solve the system with r1(0) = 1 and r2(0) =-1.

A:

Q: Solve the system dx dt x(0) with the initial value = x(t) = 19 -14 = 21 -16 -11 [] -15 x

A: The given problem is to find the solution for the given matrix differential equation with given…

Q: Arms Race: A simplified mathematical model for an arms race between two countries whose expenditures…

A:

Q: system

A:

Q: Consider a system model given by d²x (1) dt² +3- +x(t)=2- dx (1) dt x (0)=0 dx (t) dt 2- t=0 What is…

A:

Q: dx dt +2X + dy dt. +6y= 2²- 2 dx + 3x + 3 dy dt dE +8y=1

A: To solve the system of ODE. dxdt+2x+dydt+6y=2et2dxdt+3x+3dydt+8y=1

Q: Solve the system dx dt x(0) = = -22 18 with the initial value 1 x(t) = -27 23 2 8

A:

Q: 4 Classify the equilibrium is x = [0,0] for the first order system [2][3][ = 2-2 d [ x₁ (t) dt x2(t)…

A: If we denote the coefficient matrix as A,      Then, trace(A) = 1 + (-2) = -1     Determinant(A) =…

Q: Given that the three-state model equation are d[A] dt d[B] dt d[C] dt -a[A] + B[B] = = a[A] -…

A: As per the question we are given a three-state linear dynamic system and the solution for the…

Q: Solve the system dx dt x(0) with the initial value 0 1 [B] [8] = -12 5 x(t) = = -30 13 x

A: Given system of ODE  with initial value..We have to find a solution to the given system.

Q: Let x(t) = [z1(t) [r2(t). be an unknown vector-valued function. The system of linear differential…

A: As this problem is related to vector differential equation, hope you know how to find inverse of a…