Solve the wave equation using The Laplace Transformation . ( in detail please )

Expert Solution

genius_generous answered 3 months ago

3. Solve the following differential equations by using LaPlace transformation: 2x'' + 7x' + 3x =...

3. Solve the following differential equations by using LaPlace transformation: 2x'' + 7x' + 3x = 0; x(0) = 3, x'(0) = 0 x' + 2x = ?(t); x(0-) = 0 where ?(t) is a unit impulse input given in the LaPlace transform table.

Find All the following Laplace Transformations once using the definition of Laplace Transformation and then using...

Find All the following Laplace Transformations once using the definition of Laplace Transformation and then using the memorized Laplace Table relationships: L[sin⁡(ω*t)] L[(e-5t)cos⁡(6t)] L[(e-5t)(t2)]

Application of Laplace transformation in finance

solve the d.e. equation using Laplace inverse transform y'-y = xex, y(0)=0

Solve the differential equation using the Laplace transform. y''' + 3y''+2y' = 100e-t , y(0) =...

Solve the differential equation using the Laplace transform. y''' + 3y''+2y' = 100e-t , y(0) = 0, y'(0) = 0, y''(0) = 0

Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < 1,...

Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < 1, t > 0, u(0,t) = 0 = u(1,t), u(x,0) = x2, ut(x,0) = 0

Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < pi,...

Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < pi, t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinx, ut(x,0) = pi - x

Solve y'' + 16y = 7cos(4t) using variation of parameters. Then solve using Laplace transformations given...

Solve y'' + 16y = 7cos(4t) using variation of parameters. Then solve using Laplace transformations given y(0) = 1 and y'(0) = 2

. Solve the Initial value problem by using Laplace transforms: ? ′′ + 3? ′ +...

. Solve the Initial value problem by using Laplace transforms: ? ′′ + 3? ′ + 2? = 6? −? , ?(0) = 2 ? ′ (0) = 8

7. (a) Solve the wave equation in three dimensions for t > 0 with the initial...

7. (a) Solve the wave equation in three dimensions for t > 0 with the initial conditions φ(x) = A for |x| < ρ, φ(x) = 0 for |x| > ρ, and ψ|x| ≡ 0, where A is a constant. (This is somewhat like the plucked string.) (Hint: Differentiate the solution in Exercise 6(b).) ((b) Solve the wave equation in three dimensions for t > 0 with the initial conditions φ(x) ≡ 0,ψ(x) = A for |x| < ρ, and...

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