# Use the Laplace transform to solve the following initial value problem

Question

(1 pt) Use the Laplace transform to solve the following initial value problem: y″−y′−2y=0, y(0)=3, y′(0)=−3

(1) First, using Y for the Laplace transform of y(t), i.e., Y=(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)

________________+________________

(4) Finally apply the inverse Laplace transform to find y

y(t)=________________________________

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webwork / f15ndesilvam3350s010 / hw6 / 10

HW6: Problem 10

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(1 pt)

Use the Laplace transform to solve the following initial value problem: [math]

(1) First, using [math] for the Laplace transform of [math], i.e., [math],

find the equation you get by taking the Laplace transform of the differential equation to obtain

[math]

s^2Y-s+3-sY-2Y

(2) Next solve for [math] (s-2)((s+1)(Y-3))

(3) Now write the above answer in its partial fraction form, [math]

(NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to [math] and the second to

[math], where [math]. Also note, for example that [math])

[math] 3/(s+1)

+ 1/(s+1)

(4) Finally apply the inverse Laplace transform to find [math]

[math] 3e^(-t)

[math]

Note: You can earn partial credit on this problem.

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