Solve the following IVP specifically using the Laplace transform method (d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0 f''(0)=0...

Solve the following IVP specifically using the Laplace transform method

(d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0 f''(0)=0

where u(t) is the Heaviside step function

Expert Solution

milcah answered 1 year ago

using the Laplace transform solve the IVP y'' +4y= 3sin(t) y(0) =1 , y'(0) = -...

using the Laplace transform solve the IVP y'' +4y= 3sin(t) y(0) =1 , y'(0) = - 1 , i am stuck on the partial fraction decomposition step. please explain the decomposition clearly.

Solve the IVP using Laplace transforms x' + y'=e^t -x''+3x' +y =0 x(0)=0, x'(0)=1, y(0)=0

Solve this Initial Value Problem using the Laplace transform: x''(t) - x'(t) - 6x(t) = e^(4t),...

Solve this Initial Value Problem using the Laplace transform: x''(t) - x'(t) - 6x(t) = e^(4t), x(0) = 1, x'(0) = 1

1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)=...

1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)= 3) Find the Laplace transform of f(t)=u(t−6)⋅t^2 F(s)=

Solve the partial differential equation by Laplace transformu_x (x,t)+u_t (x,t)=e^3t given that u(x,o)=0 , u(o,t)=e^3t

Solve y"+y=u(t-pi/2)+3 delta(t-3 pi/2)-u(t-2 pi), by laplace transform methods with y(0)=y'(0)=0.

Find the Laplace transform of the following functions. (a) f (t) = { 6 0 < ...

Find the Laplace transform of the following functions. (a) f (t) = { 6 0 < t ≤ 4 8 t ≥ 4 (b) f (t) = { t2 0 ≤ t < 3 0 t ≥ 3 (c) f (t) = { 0 0 ≤ t < π/4 cos[7(t − π/4)] t ≥ π/4

Solve this Initial Value Problem using the Laplace transform. x''(t) + 6 x'(t) + 25x(t) =...

Solve this Initial Value Problem using the Laplace transform. x''(t) + 6 x'(t) + 25x(t) = cos(t), x(0) = 0, x'(0) = 1

Find the laplace transform of the following functions, using the definition of Laplace transforms: f(t)=-2cos4t f(t)=2...

Find the laplace transform of the following functions, using the definition of Laplace transforms: f(t)=-2cos4t f(t)=2 sin^2(t) g(t)=3e^tcos(t)

Solve the IVP: u'' + 10u' + 98u = 2sin(t/2) u(0) = 0 u'(0) = 0.03...

Solve the IVP: u'' + 10u' + 98u = 2sin(t/2) u(0) = 0 u'(0) = 0.03 and identify the transient and steady state portions of the solution. Plot the graph of the steady state solution.

Question