Use Laplace transforms to solve the initial value problem. "1 y"+ 8y + 15y=0; y(0) = 2, y '(0) = -3 L{f(n))=sF(s)-f(0) L{ƒ¨(t)} = s²F (s) — sf (0) — ƒ '(0)

Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

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Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

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Q: Let A(x) be the function defined by A(x) = 4 We have A(0) = -3 A'(-1/2) = -2 for x = [-1,0], A(x) =…

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Q: Find the differential quotient of the following functions: a) f(x)=5x–2 b) f(x)=x2 +3 c)…

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Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: Find the first and second order derivatives of the function (a) f(x) = 0.001x5 -0.002x³ (b) G(r) =…

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Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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Q: 4. The equation (x – y)² = x + y – 2 defines a function y = f(x) in a neighborhood of (1,2). Use…

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Q: Compute the derivative of f(x) = ( sin(2x + 1))/°. 4 (sin(2x+ 3 1) -1/3 • cos (2x + 1) 4 -1/3…

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Q: Find f'1, f'2, f'1 (4,5), and f'2(1, - 6) for the following equation. f(x.y) = /x2 +y² 2+y? f'1 =…

A: Notations and terminologies: For a given function g(x,y) ∂g∂x=gx=g1'∂g∂y=gy=g2'

Q: Find the differential of each function. (a) y = 2 + 55 dy (5s + 2)² (b) y = eu cos(u) 1. dy =…

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Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: Let Q (p) : %3D p+1 (a) Calculate the derivative Q' (p) (b) Calculate the quotient Q (p + 4) – Q (p)…

A: Using derivative formula.

Q: p(s) SIMPLIFY COMPLETELY. 9(s) Find Y(s) in the form y" +3y' + 2y = 0 y(0)=1 y'(0)=2

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Q: A) Find the first and second derivatives of the function g(x) = Vx² + 2x .

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

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: 1) Consider the functions ƒ(a) = 100 – 2¹ª and F(x) = f(t 1² f(t) dt. i. Write a simplified form of…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: y''-3y'+10y=e-2t , y(0) =0, y'(0)=1

A: We have to solve given problem:

Q: Calculate the first, second, and third derivatives of y(t) = 2016/5 – 6127. (Use symbolic notation…

A: We will use simple differentiation rules to solve this question.

Q: x) such that f"(x)=2r' +3x-4

A: Integration: f''(x)=2x3+3x2-4x+5; f0=2, f1=0 ∫xndx=xn+1n+1+c

Q: Find an equation of the tangent line for the following functions at the given points x-2 a. y= at a…

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Q: By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) =…

A: The differentiation of a definite integral can be obtained by using the Chain Rule following…

Q: 1. Use the basic differential properties shown in section 3-5 to find each indicated derivative. (A)…

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…