Out of the systems shown below, which one is non-causal? y(t) = -x (t) dy (t) dt A. B. C. D. dy(t) dt + t⋅u(t).y(t) = x (t) +y(t) = x (t+1) dy (t) + y² (t) = x(t) dt

Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

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Q: S [x, y] = 1 dt (x² + y²+xÿ), x(0) = y(0) = 0, x(1) = X, y(1) = Y. = √² dt S Hence show that the…

A: Let us consider a variational problem S[x(t),y(t)]=∫abdt F(x,y,x′,y′) , then the necessary and…

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Q: If r(t) = (1,r ,t), then r'(t) equals (a) (1,21,-2r"). (b) (0,21,–21 ") . (e) (0,21,-21 *).

A: Given that: r(t)=1,t2,t-2Differentiate both sides with respect to…

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

A: Given system of differential equation:

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Q: Determine the local stability of equilibrium of the ODE d = x(t) = x² − y dt d y(t) = x(y = 2x). dt'

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Q: t=-2 t=-1 t=0 t=1 t=2 *=97² +9t, x=9t² +9t, y=3t+ 1 (x, y) = (x, y) = (x, y) = (x, y) = (x, y) =

A: Given that  Then, we have to find  for different value of t.

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A: Solution :-

Q: Minimize c = s + t + u subject to 3s + 2t + u ≥ 48 2s + t + 3u ≥ 48 s + 3t + 2u ≥ 48 s ≥ 0, t ≥ 0, u…

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Q: Let f(x, y) =x+3x2y2, x(t) =t2 and y(t) =t3. Find F(x(t), y(t)) F(x(0),y(0)) F(x(2),y(2))

A: Let f(x, y) =x+3x2y2, x(t) =t2 and y(t) =t3

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Q: Find the particular solution of y2dx + x(x+y) dy=0., when x=1, y=1. Let x=vy

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Q: Two species named P and Q have populations given by P(t) and Q(t) respectively. Their interaction is…

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Q: dy Identify P (x) in the given linear equation: x- + x°y = 5x %3D da OP(x) = x O P (x) = x2 O P (x)…

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Q: a. Let x(t) = u(t + 1) + 2u(t− 1) + u(t− 2) and h(t) = 28(t+1) +28(t-1) compute and plot y(t) =…

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Q: (a) Let r(t) = ti+tej+fk. Find ((1),4 × (?),1) - (1)a tuj

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Q: Show the function T : R² → R³ given by T(x, y) = (x − y, 3x + 2y, 0) is linear.

A: The given function  is given by .To show that T is linear.