Question

Use the Laplace transform to solve the following initial value problem: y'' - 6y' + 8y = 0, y(0) = 2, y'(0) = 4 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain = 0 (2) Next solve for Y = (3) Now write the above answer in its partial fraction form, Y = A / (s - a) + B / (s - b) (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that -2 < 1) Y = + (4) Finally apply the inverse Laplace transform to find y(t) y(t) =

          Use the Laplace transform to solve the following initial value problem: y'' - 6y' + 8y = 0, y(0) = 2, y'(0) = 4
(1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)),
find the equation you get by taking the Laplace transform of the differential equation to obtain
= 0
(2) Next solve for Y =
(3) Now write the above answer in its partial fraction form, Y = A / (s - a) + B / (s - b)
(NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b.
Also note, for example that -2 < 1)
Y = + 
(4) Finally apply the inverse Laplace transform to find y(t)
y(t) =

$Use the Laplace transform to solve the following initial value problem: y” - 6y' + 8y = 0, y(0) = 2, y'(0) = 4 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain = 0 (2) Next solve for Y = (3) Now write the above answer in its partial fraction form, Y = A / (s - a) + B / (s - b) (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that -2 < 1) Y = + (4) Finally apply the inverse Laplace transform to find y(t) y(t) =$

Added by Soledad G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kumareshwaran Rathinasabapathy

02/24/2022

Step 1

Step 1: Take the Laplace transform of the given differential equation: The Laplace transform of y'' - 6y' + 8y = 0 is given by: \[ Y(s) = s^2Y(s) - 6sY(s) + 8Y(s) \] Show more…

Show all steps

Thanks for your feedback!

Use the Laplace transform to solve the following initial value problem: y'' - 6y' + 8y = 0, y(0) = 2, y'(0) = 4 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain = 0 (2) Next solve for Y = (3) Now write the above answer in its partial fraction form, Y = A / (s - a) + B / (s - b) (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that -2 < 1) Y = + (4) Finally apply the inverse Laplace transform to find y(t) y(t) =