Solve the following wave equation using partial Laplace transform: a²ua²u + sinxx; 0≤x≤ 1, tz0 at² ex² u(x,0) = 0,2(x,0) = 0 at u(0, t) = 0, u(1, t) = 0

Q: ikt 三 ik ik Ikt. ik こ

A: So we have to solve the inverse Fourier transform to get the expression for U(x,t)

Q: What is the laplace transform of f(t) = cos t u(t-1)?

A:

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: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

A:

Q: Find the Laplace transforms of the functions. f(t) = Cos^2(2t)

A: Let ft=cos22tTo find: Laplace transform of the function ft.