Question

In: Advanced Math

Use Laplace transform and inverse Laplace transform to solve the givien initial value problems (c) y′′...

Use Laplace transform and inverse Laplace transform to solve the givien initial value problems

(c) y′′ −2y′ +2y=e−t, y(0)=0, y′(0)=1

Solutions

Expert Solution


Related Solutions

Use Laplace transform method to solve the following initial value problems (a) d2y/dt2 + y =...
Use Laplace transform method to solve the following initial value problems (a) d2y/dt2 + y = e^ −t ; y(0) = 0, y′ (0) = 0. (b) d2y/dt2+ y = t subject to the initial conditions y(0) = 0, y′ (0) = 2 (c) dy/dt + 2y = 4e 3t subject to the initial condition y(0) = 1.
Use the Laplace transform to solve the following initial value problem, y′′ − y′ − 30y  ...
Use the Laplace transform to solve the following initial value problem, y′′ − y′ − 30y  =  δ(t − 7),y(0)  =  0,  y′(0)  =  0. The solution is of the form ?[g(t)] h(t). (a) Enter the function g(t) into the answer box below. (b) Enter the function h(t) into the answer box below.
Apply the Laplace Transform to solve the initial value problems 1. y' + 2y = 2cos(3t)...
Apply the Laplace Transform to solve the initial value problems 1. y' + 2y = 2cos(3t) , y(0) = 1 2. y'' - 3y' + 2y = 2 - 10e-3t , y(0) = -1 , y'(0)= 1
Use the Laplace transform to solve the given initial-value problem. y'' + y = δ(t −...
Use the Laplace transform to solve the given initial-value problem. y'' + y = δ(t − 6π) + δ(t − 8π), y(0) = 1, y'(0) = 0
8) Use the Laplace transform to solve the given initial-value problem. y' − y = 2...
8) Use the Laplace transform to solve the given initial-value problem. y' − y = 2 cos(4t),  y(0) = 0 y(t)=??? 9) Use the Laplace transform to solve the given initial-value problem. y'' − 5y' = 8e4t − 4e−t,    y(0) = 1, y'(0) = −1 y(t)=? 10) Use the Laplace transform to solve the given initial-value problem. y''' + 2y'' − y' − 2y = sin(4t),  y(0) = 0,  y'(0) = 0,  y''(0) = 1 y(t)=?
Use the Laplace transform to solve the given initial-value problem. y'' − 7y' = 12e6t −...
Use the Laplace transform to solve the given initial-value problem. y'' − 7y' = 12e6t − 6e−t,    y(0) = 1, y'(0) = −1
Use the Laplace transform to solve the given initial-value problem. y'' + 6y' + 34y =...
Use the Laplace transform to solve the given initial-value problem. y'' + 6y' + 34y = δ(t − π) + δ(t − 3π), y(0) = 1, y'(0) = 0 y(t) =( ? )+ ( ? )· U (t − π) + ( ? )· U (t − ? )
Use the Laplace transform to solve the given initial-value problem. y'' - 2y'' - 8y =...
Use the Laplace transform to solve the given initial-value problem. y'' - 2y'' - 8y = 2sin2t; y(0) = 2, y'(0) = 4
Use the Laplace transform to solve the given initial value problem. y(4) − 4y''' + 6y''...
Use the Laplace transform to solve the given initial value problem. y(4) − 4y''' + 6y'' − 4y' + y = 0; y(0) = 1, y'(0) = 0, y''(0) = 0, y'''(0) = 1
Use the Laplace transform to solve the given initial value problem. y(4) − 4y''' + 6y''...
Use the Laplace transform to solve the given initial value problem. y(4) − 4y''' + 6y'' − 4y' + y = 0; y(0) = 1, y'(0) = 0, y''(0) = 0, y'''(0) = 1
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT