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

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Find the Laplace transform of d2y/dt2

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

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.

Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt +...

Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt + 2y = 6 exp(3t), y(0) = 6, y’(0) = 14.

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)=?

Question