Solve by Laplace transform Utt – 9urz = 0, 0 0 %3D u(0, t) = u(r, t) = 0, %| %3D u (x, 0) = 0, u(x,0) = 2 sin x.

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

Q: Find the general solution of the DE s

A: Given: - The differential equation is, dydx=2yx+x3y+xtanyx2 To find: - The general solution of the…

Q: Find the Fourier Transforms of the indicated function: f (x) = cos x e−x^2/2

A: The given problem is to find the Fourier transform of the given function. Given function, f(x) =…

Q: Use Laplace transforms to solve the IVP y''-y=0, y(0)=2, y'(0)=3. Show the complete solution.

A: Given initial value problem is, y''-y=0, y(0)=2, y'(0)=3

Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=2.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: What is the Fundamental period of cos(r)? Select one: а. 2т у b. 37 C. T O d. I am not sure (yet)

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Q: س1/ حل التكامل التالي dx (x + 2) Vx2 + 4x+ 3

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Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: Find the maximum value of  sinx+cosx at [0,pi]

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Q: apply shifting property of laplace in the equation f(t)= t cos 2t and f(t)=t^2e^-3t

A: To apply the shifting property of Laplace in the given equations.

Q: Solve equation using Laplace transform ÿ +9y = 6 (t -) sin(t), y(0) = 0, y(0) = 0 %3D

A: Given the given equation is y"+9y=δt-π6sint,     y0=0,  y'0=0 Use the property of delta function.…

Q: QI\ Find Fourier transform for: A) f(t) = U(t)sin² (3t) C) f(t) = elct sinh(bt)

A: (A)Given the function f(t)=u(t)sin2⁡(3t).Rewriting, .We know that, .The Fourier transform of f(t) is…

Q: Find dy/dx for x⁴+siny=x³y²

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Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=<t sin t+cos t,2t2,sin t -t cos y> Then vector is given by r→t=t sin t+cos…

Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=5.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: Compute sin (3r)dr (25z4+1)2 -

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Q: Express the integral / rV1: V125 – 23 dr in terms of Beta function.

A: The solution is given as

Q: The laplace transform of f(t) = t^3 (sinh 2t − cos 2t)

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Q: Solve using Laplace transform technique y"+ 4y = 9t, y(0) = 0, y(0) = 7 %3!

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Q: Find the linearization at x=a and then use it to approximate f(b) 1.) f(x)=x4, a=1, b=0.96

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