26.Show that if p is differentiable and p(t) > 0, then the Wronskian W(t) of two solutions of [p(t) y′]′ + q(t) y = 0 is W(t) = c/ p(t), where c is a constant.

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A: We are given a IBVP and we will use separation of variables to solve it.

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A: The function for state feedback control is J=∫01x2+u2dt The value of x¯is -x+u and x(0) is 2.

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. S 1, 0sx s 1 x > 1…

A: Given that dydx+y=fx  , y0=1  fx=1  ,0≤x≤1-1    x>1Solution:When 0≤x≤1dydx+y=1 this is the linear…

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Q: Solve the fallowing Cauchy problem U4- Au + cu=0 in R" x(0, 0) On IR"x{t=0}. U = where c is a…

A: Given the Cauchy problem as ut-∆u+cu=0,             in ℝn×0,∞                (1) re-write the…

Q: 1 The linear approximation at = 0 to is V2 – x A + Bx where A is: and where B is:

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A: This is a problem of IVP.

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

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A: An explicit solution is any solution that is given in the form y=y(x)

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A: Problem is solved using concept of fourth-order runge-kutta method.

Q: 1. Determine the types of the following partial differential equatio: (a) 4upa - 4uæy + Uyy 4uxy (b)…

A: According to the guidelines I am answering only first question.

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Q: 9. (a) Use the method of Lagrange multipliers to determine the minimum and maximu values of f(x, y)…

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + y = f(x), y(0)…

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Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

A: Given the Cauchy problem as  ut-∆u+cu=0,       in ℝn×0,∞           (1) re-write the equation (1) in…

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Q: Solve the following initial-boundary / boundary value problem. ди u, 0 0, ди ди (0, t) = o" (1, t)=…

A: To find- Solve the following initial-boundary / boundary value problem. ∂u∂t = ∂2u∂x2 - u,…

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A: GIVEN: y = c1 + c2 x2

Q: 2. Find the Wronskian for the given Y" +5Y +4Y = 0, Where two solutions are y, = e-4t , and y2 = e-t…

A: We use the definition

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Q: 14.Consider the equation dy/dt = f(y) and suppose that y1 is a critical point—that is, f(y1) = 0.…

A: Draw y vs. f(y) graph with the phase line on some interval y1-e, y1+e 1. f'y1&lt;0 fy is decreasing…

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Q: (j) Suppose that the solution of the initial value problem u" + u = 0.5 cost, u(0) = 0, u'(0) = 0 is…

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Q: 1. Consider the initial value problem y' = 3y + 1, y(0) 2. %3D %3D (a) Show that all the successive…

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Q: 1. For u(x, t) defined on the infinite domain of -o 0, solve ди with boundary conditions: u(x, t)…

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Q: #3. Solve the fallowing Caucly problem in R" x(0, 0) Uf-Ou t cu =0 on IR"x{t =0}. U = where c is a…

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