2. Solve the optimal control problem max { J(u): = [ (3e(t) – 2u(t)dt> subject to the dy- 2u(t))dt > subject to the namics dx = x(t) + u(t), dt x(0) = 5, 0

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

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Q: 2) Create a direction field plot for the logistic equation dP dt = 2 P(1 - 1) on the rectangle 0 ≤ ≤…

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Q: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

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Q: +3+10y = 13e-t, y (0) = 7, (0) = 11 and using Euler's method and a step size of 1.5, y (3) is most…

A: 2d2ydt2+3dydt+10y=13e-ty0=7dydt0=11 Step size h=1.5

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

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Q: Suppose the control problem is Maximize [(y-²)dt 0 Subject to y'=u and y(0) 10, y(1) = a = The…

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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 the IVP dx dt [ x(t) = 12 0 X, -24 0 x(0) = [13] 181

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Q: 28. Consider the autonomous equation dy/dt ferentiable, and suppose we know that f(-1) = f(2)= 0. =…

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Q: 12:06 ■I 5G (8) If f(z) = √1+dt and g(y) = f (x)dx then find g"(#/3).

A: Thank you

Q: 4. In one model of the changing population P(t) of a community, it is assumed that dP dt dB dD dB…

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Q: Solve for P(t) using the given information. d² p dt² = (6t, 2+3t), P(1)=(2,1), P'(1)=(3,2)

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Q: Solve the IVP dx dt x(t) = -12 0] 1]* 118 -24 0J - x, x(0) = 1 -18

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

Q: (iii) XF= F-1 – DT.

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