Let f(t) be a continuous function on (-∞,). Show that the particular solution to the equation U 4y"+y=f() is y,0)=ff(t-u) sin du. 2

Q: Find y as a function of a if y(0)2, y'(0) = 3, "(0) = -13. y(x) = y″ − 4y″ − y′ + 4y = 0,

A: Given a differential equation:initial conditions are:

Q: 8. Find directional derivative of function z = xey at point P(1,0) in the direction from pointP(1,0)…

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Q: Let f(x) = (4e" +h(x)) h(x). Assume that h(2) 4 and h' (2) = 1. Find f'(2). And, find the tahgent…

A: Equation of the tangent line

Q: h" (t) = sec? t – Vt, h(0) = -3, and h'(0) = 3. %3D

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Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

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Q: Find y as a function of t if y(4) = 6, y (4) = 4. y = 121y" - 132y +36y = 0,

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Q: Let h = fog where ƒ : R² → R and g: R² R² is defined by g(x, y) = (3x²y, x – 2y). Find the…

A: Letandfind the derivative

Q: Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x 1.

A: You have posted multiple question. As per the instruction, we are answering the first one. If you…

Q: find the first and the second derivative of these equation , first as a function of z then as a…

A: Given: Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: How to solve this equation y'''-4y''+2y'-8y=6e^(x) - x^(2) + 1 using Methods of Undetermined…

A: Given: Given differential equation is y'''-4y''+2y'-8y=6ex-x2+1 We will solve this equation using…

Q: Find the derivative of the function at P, in the direction of A. f(x,y) — - Зху + 4y*, Po(-6, - 5),…

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Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: -1 A = 0 2) 0. x)T. F(e,) = ( 2

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Q: 9. For each n E IN, let Xn be the set of polynomials of degree equal to n, and let Pn = U_0 Xk. True…

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Q: 3) f(t) = t*e?t %3D

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

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Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Find y as a function of x if y(0) = 13, y' (0) = 22, y" (0) = 27. y(x) = y" - 15y" +56y' = 42e*,

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Q: At the point (1, −1), the function (x, y) has a derivative of 5 in the direction toward (3, 1) and a…

A: Consider the given information.

Q: Use L and L to solue y' t 3y= f4) y)=5, where f4), (32)

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Q: 1. Determine whether the given functions are differentiable (anywhere). If the function is…

A: We will check where given function is differentiable and then we will find the derivative of…

Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

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Q: Let f(x) = 2 – 2², x > 0 f'(x) = Preview

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Q: Find y as a function of x if y" + 16y' = 0, y(0) = 0, y'(0) = 4, y'(0) = -32. y(x) =

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Q: Suppose f, g have the following values: f(3) = e5 and g(3) = 2. ƒ'(3) 10 and g' (3) = = 8. 4 Let y¹…

A: To find the value of y' at (3,-3).