Consider the following initial value problem: y" + 4y = sint − u2(t) sin(t — 2π); y(0)=0, y'(0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval. -1 y(t): m/4 = P (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by uc(t) where uc(t) = 1 if t≥c and 0 otherwise. Indicate separately the value of c. where c = 5/4 3/2 7/4 2 9/4 5/2 1/4 3 X X X

Q: Consider the graph of the function given in the image: Knowing that L {x (t)} = X (s). Find X (s)…

A: We find X (s) from the following initial value problem:   x''-2x'+x=et f(t) with x(0)=4 and x'(0)=0

Q: 1. An object is moving along a straight line and its velocity at time t is given b v(t) = t² − 4t -…

A: Given :- ⇒vt=t2-4t-5 By completing square method ⇒vt=t2-4t+22-22-5 ⇒vt=t-22-9 vertex (2,-9)

Q: 4. (a) An object with a velocity, v, falls under gravity from rest (t = 0, v = 0) as defined by: dv…

A: The given DE is linear first order DE.

Q: Consider g(y)=y4/4+1/8y2. (a) Find the derivative. (b) Find the expression for 1+[g′(y)]2. (c)…

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Q: 3. Find the position function x(t) given the acceleration a(t), the initial velocity vo = %3D v(0),…

A: It is given that the acceleration function is at=6t+4. The initial velocity at t=0 is v0=v0 and the…

Q: (1) Assume the velocity of a particle at time t is given by the function v(t) = (3 + 4t, 5 – 7t,…

A: The velocity function of the particle at time t is  v⇀(t) = (3 + 4t , 5 - 7t, 11t) which can be also…

Q: (A B Which of the following functions satisfy x²dy + y(x + y)dx=0 with y(1) = 1 ? 3x²y = 2x + y x²y…

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Q: Consider the equation a"(t) + 2a'(t) + 5æ(t) = cos(at), where a is a real number. (a) Find the…

A: since you have posted multipart question but according to guidelines we will solve first three sub…

Q: 1: For each of the functions below, decide whether it solves the equation: (y)² = 1 - y². A) y(t) =…

A: Given that the differential equation is .The objective is to verify the given solutions.

Q: 3. (a). For a curve defined by an equation f(x), satisfy dy + (1 – 2x)y = 4x for x > 0 and - dx f(1)…

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Q: Let z(t) = 5 cos (t) and y(t) = 3 sin(t) ELLIPSE 2- At t = 3, x(3) = -495 -1- y(3) = 0.42 -2- dz…

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Q: Jx + 2x f(x)=- 7х — 4х? 8.

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Q: II. Consider the function g defined by 9(z, y) = cos (7z/T) logg(z Do as indicated. In what…

A: We know that the gradient of the function g contains the two vectors, one in the direction of x-axis…

Q: 3. Find all the first and second order partial derivative of the function: z(x, y) = sin(Mx) cos(Ny)…

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Q: Consider the graph of the function given in the image: Knowing that L {x (t)} = X (s). Find X (s)…

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Q: Solve for the gradient 1. F = x²yi - (2³-3x)j + 4y²³ k · F¹ = (3x + 2z²) i + ²³y² 3 − ( 2. 3.…

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Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: erivative of the following functions. (a) f(t)= e + 2t² df/dt = (b) f(t) = sin(3t) + 4 df/dt = (c)…

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Q: Find g'(9) given that f(9) = 5 and f'(9) = 1. Enter the exact answers. (a) g (x) = Vaf(x) %3D g' (9)…

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Q: (3) Let 4 = x²y² + x sin y, find 2 dy in terms of x and y; dx (4) Find the equation of the tangent…

A: For the given problem, there are two questions. But according to rules of Bartleby only the first…

Q: Consider the graph of the function given in the image: Knowing that L {x (t)} = X (s). Find X (s)…

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Q: Assume that G(x.y)=c is an implicit function, where c is constant. Which of the following equations…

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Q: Let f(æ) = 12a + 3 - 17e". Then the equation of the tangent line to the graph of f(x) at the point…

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Q: b) Find the Green's function for the operator £y(x)= y (1) = 0. (x + y(x))* with y (0) finite and dx…

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