By using Laplace transform to solve y" + 4y + 8y = sint with y (0) = 1 and y' (0) = 0, what would be F (s) equivalent to?

Q: h(x)=3sinh(1–3x² )cosh(1–3x² )

A: Sinh^-1(x)= ln(x+[√x^2+1]) Cosh^-1(x)=ln(x+[√x^2-1])

Q: Find f. f(0) = = f"(0) = sin(0) + cos(8), f(0) = 3, f'(0) = 2

A: f"θ=sinθ+cosθ Integrating both sides  ∫f" θdθ=∫sinθdθ+∫cosθdθ f'θ=-cosθ+sinθ+C..... (i)  Put θ=0…

Q: 4 Use implicit differentiation to solve for y' if r4y2 - x³y + 2xy³ = (Show your work)

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Q: JO (5) Find the derivatives (a) d # t ( * cos(2³) dz + 35e) 4

A: Since you have posted multiple questions i can do first question as per our company guidelines.…

Q: 2 5. x=- 1+t2 2 y=, t(1+t?)

A: Given: x=21+t2, y=2t(1+t2).

Q: Let y -2 = S sin³ (t) dt. Use the Fundamental Theorem of Calculus to find y'. ex

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Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: If t²y" – ty – y = 0 ,y(1) = 3 and y'(1) = -1, then y(4) = . . . %3D

A: Given differential equation, t2y''-12ty'-y=0,y1=3,y'1=-1 Find the value of y4.

Q: Apply the method of Example 6 to f (x) = sin x to determine f ' ( π/4 ) accurately to four decimal…

A: Given function is fx=sinx. To determine f'π4. Solution: Function is fx=sinx. Differentiating the…

Q: d mula sinh (t) = In (t + VE? + 1) and- (In(t)) = } %3D ne derivative of sinh(t).

A: Here we use rule of differenciation to find the required derivative.

Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: Find f. f"(x) = x³ + sinh(x), f(0) = 4, f(2) = 5.6

A: f'' ( x ) = x3 + sinh(x)   , f ( 0) = 4, f ( 2 ) = 5.6    To Find: f ( x )

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: Find the solution for this second ODE y(0) = 1, y'(0) = 1

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Q: Differentiate h(y) = ln (3y) sin y

A: To differentiate the function  h(y)= ln(3y)sin-1y

Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: Find f. f(x) = f"(x) = x3 + sinh(x), f(0) = 1, f(2) = 2.6 ×

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Q: F(s) = Le 4t cos(5t)}

A: We have to find  ℒe-4tcos5t Remember : ℒeatf(t)=Fs-a where  ℒf(t)=Fs

Q: If g(x) = | cos' t dt , then determine g'(x). %3D

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Q: Find y' 1. (x-y)2 = sin x + sin y

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: (z2)juə = (x)/ sin(#x). Compute f'(x). %3D

A: We will solve the problem

Q: If f(x) 3 sin '(2), then f'(x)-

A: Given that: f(x)=3sin-1(x5)

Q: Find a root of f(x) = 6 Sin (x)e- x + 1 using Newton Raphson Method accurate to 5 decimal places.

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Q: Let f(x) = 4x - 32√x and a = 4. Compute f'(x) and find an equation for the tangent line to the graph…

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Q: Sin (7€) + Cos (SE) 5지

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Q: _et f(x) = Then f'(x) = 6 sin 6 sin x + 4 cos π The equation of the tangent line to y = f(x) at a =…

A: fx=6sinx6sinx+4cosx