(i) Solve the linear system below using Laplace Transforms dx =-aX+Y₁ dt for some real constant a, and X(o)=0, Y (0) = 1 dy dt =X-ay

Q: How to find the characteristic equation of the system: dx(t)/dt=Ax(t) + Bu(t)

A: To find the characteristic equation of the system:

Q: Determine the local stability of equilibrium of the predator prey model x(t) = x -0.5xy (t) = 3xy —…

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Q: zow(t)dt = zo / w(t)dt. 2. a. [w(t) + W(t)]dt = | w(t)dt + | w(t)dt 3.

A: The general formula for the integration is I=∫abf(x)dx. Here, a is the lower limit and b is the…

Q: (E) 18. Consider the function f = e2"y – xy tan 3x+7. Compute the gradient of f, and compute all…

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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

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Q: Determine the local stability of equilibrium of the ODE d dt x(t) = x(1−xy) dt³ (t) = y=x².

A: Given, a system of ordinary differential equations:It is required to find the local stability of the…

Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. dx 4x² - x³ dt 3 The…

A: We need to find the equilibrium at x=0 is stable, unstable, or semi stable. given,…

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: 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: 1. f(x) = x², g(x) = 4|x]? %3D %3D 2. f(t) = 212 + 14t , g(t) = 2f² – 14t 3. f(0) = cos(30), g(0) =…

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Q: X Suppose Suppose f(t)dt = x - 9x + 8. Find f(x). 3 f(x) = 1

A: This question can be solved using the concept of first fundamental theorem of integral calculus.

Q: Find all the second order partial derivatives of the given function. f(x, y) = In (x 2y - x) O a2f…

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Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t     x(t) general function solutions

A: This system has been solved by the elimination method, by eliminating y to get the general solution…

Q: Find the required first- and second order partial derivatives of the function f(x, y) = ln (x² +…

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Q: Bruce and Cruz had 294 bookmarks altogether. Bruce gave away 3/8 of his bookmarks and Cruz gave away…

A: Let the number of bookmarks Bruce has = B The number of bookmarks Cruz has = C therefore B+C=294…

Q: dx dy 2- + dt dt dx dt —— -4x - y = et... (1) +3x+y = 0 ............. (2)

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Q: Find the general solution of (a) dy = ty(1+ t²)-1/2 dt (b) fip' dt + (t + 2)y = 1

A: To find the general solutions of given differential equations

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

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Q: d²x dt² dx +vf(x). + g(x)= 0, v ≥ 0, dt where f(x) and g(x) are well behaved functions and a…

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Q: 1. The first order linear method workflow is described in dx + a(t)x = f(x) dt dx the table to the…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Given the transfer function H(s) Find y(t) when x(t)=d(t) s+2…

A: Sol:- First find the h(t) using Inverse Laplace Transform:- L-1s+2s+12+4=L-1s+1s+12+4+1·1s+12+4Use…

Q: Linear First-Order D.E. Solve the equation: (t + y + 1) dt - dy = 0

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Q: Solve the 2 × 2 ODE system dr -x³ + Y• dt dy dt

A: Given 2×2 ODE system, dxdt=-x3+ydydt=-y3-x Since both the functions -x3+y and -y3-x are…

Q: Consider a delayed logistic equation of the form z(t + At) = z(t) + ar(t) (1– z(t – 2At)' K (a)…

A: Given: Let us consider the given delayed logistic equation of the form, xt+∆t=xt+αxt1-xt-2∆tK and…

Q: 20 -24 dx dt 16 -20 with the initial value x(0) 4 x(t) =

A: Consider the provided question,

Q: 0.125 А. f(8t) dt | 0. 0.25 B. f(1 – 4t) dt = 2.5 c. f(5 – 2t) dt =

A: Given that,

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…

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Q: Prove if y(t): = Yı(t) Y₂(t) such that y(0) = []; satisfy = Ay; t > 0 dy dt ; where A is 2 x 2…

A: yt=y1ty2tdydt=Ay; t>0y0=01trA=0DetA>0

Q: Find a function f and a number a such that f(x) = a-7 f(t) + f² d t4 1+ -dt = 6x-¹ -1

A: NOTE: Refresh your page if you can't see any equations..take derivative on both sides

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: Use substitute method to solve the two system ec -= x - 4y (1) dx #1: dt dy -= x+y (2) dt

A: As per our guideline we supposed to answer only first question  Given system dxdt=x-4y…

Q: We know that: Theorem (*) If y₁, y₂ are linearly dependent on some interval, and their derivatives…

A: Theorem (*) : If y1 , y2 are linearly dependent on some interval and derivatives y'1 and y'2 exist…

Q: ) A metal component is subjected to heat-treatment called normalisation. The component is eated to a…

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Q: Find y(t) given the following transfer function: Y(s) = (s+2) (s+4) s(s+1)(s+3)

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Q: given: v=(3t - x)e-2t 1. find (d2v)/(dt2) 2. find (d2v)/(dtdx) complete solution

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Q: Using Lyapunov's method to dtermine the st. for the following systems. dx dt dy dt -2y - x5, 3x -…

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Q: P1: The output y(t) of a causal linear time invariant system is related to the input x(t) by the…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…