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Solve the initial value problem below using the method of Laplace transforms y"-y'-12y= -7cos(t)-5sin(t), y Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms y(t)= (Type an exact answer in terms of e.) Solve the initial value problem below using the method of Laplace transforms y"+5y'+6y= -5 cos(t)-2sin(t), Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms 24-2[1-31-3[-3 3 y(t)= sin(t) 10e 10 10 (Type an exact answer in terms of e.) I have submitted this question to Chegg several times and been given an incorrect answer every time, so please listen carefully. Below the question I need answered I have attached an example problem of the same problem with different numbers. Notice how the answer is formatted in the example question and notice the (t-pi/2) in the exponents. This directly relates to how you solve the equation. The answer to my question should be formatted very similar to the example answer beneath!!!!! REREAD THESE INSTRUCTIONS BEFORE ATTEMPTING TO SOLVE.

          Solve the initial value problem below using the method of Laplace transforms
y"-y'-12y= -7cos(t)-5sin(t), y
Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms
y(t)= (Type an exact answer in terms of e.)
Solve the initial value problem below using the method of Laplace transforms
y"+5y'+6y= -5 cos(t)-2sin(t),
Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms
24-2[1-31-3[-3 3 y(t)= sin(t) 10e 10 10 (Type an exact answer in terms of e.)
I have submitted this question to Chegg several times and been given an incorrect answer
every time, so please listen carefully. Below the question I need answered I have attached an
example problem of the same problem with different numbers. Notice how the answer is
formatted in the example question and notice the (t-pi/2) in the exponents. This directly relates
to how you solve the equation. The answer to my question should be formatted very similar to the example answer beneath!!!!! REREAD THESE INSTRUCTIONS BEFORE ATTEMPTING TO
SOLVE.

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solve the initial value problem below using the method of laplace transforms y y 12y 7cost 5sint y click here to view the table of laplace transforms click here to view the table of properti 36737

Added by Thomas B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linda Hand

04/04/2022

Step 1

The Laplace transform of y" is s^2Y(s) - sy(0) - y'(0). The Laplace transform of y' is sY(s) - y(0). The Laplace transform of -12y is -12Y(s). The Laplace transform of -7cos(t) is -7(s/(s^2+1)) - 5/(s^2+1). So, the Laplace transform of the given differential Show more…

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Solve the initial value problem below using the method of Laplace transforms y"-y'-12y= -7cos(t)-5sin(t), y Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms y(t)= (Type an exact answer in terms of e.) Solve the initial value problem below using the method of Laplace transforms y"+5y'+6y= -5 cos(t)-2sin(t), Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms 24-2[1-31-3[-3 3 y(t)= sin(t) 10e 10 10 (Type an exact answer in terms of e.) I have submitted this question to Chegg several times and been given an incorrect answer every time, so please listen carefully. Below the question I need answered I have attached an example problem of the same problem with different numbers. Notice how the answer is formatted in the example question and notice the (t-pi/2) in the exponents. This directly relates to how you solve the equation. The answer to my question should be formatted very similar to the example answer beneath!!!!! REREAD THESE INSTRUCTIONS BEFORE ATTEMPTING TO SOLVE.

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Transcript

00:01 All right, i'm going to solve this differential equation by taking the plus transform of both sides, and then i'm going to simplify it, and then i'm going to inverse the plus transform.

00:13 So i need l of y double prime, plus 2, l of y, plus, oh, y prime, plus 8, l of y, equals l of 0, which is a 0.

00:30 All right, so l of y prime, that's right here.

00:36 So s squared big y minus s times y of zero, which is minus 1, minus y prime of 0, which is 10, plus 2 times l of y prime prime, that's this one, 2sy minus y of 0, which is minus 8y prime, that's this one, 2sy minus y of 0, which is minus 1, plus 8y.

01:04 Equals 0.

01:07 So s squared plus 2 s plus 8 big y plus s minus 10 plus 1.

01:20 So minus 9 equals 0.

01:24 Did i get everybody? s squared 2s 8.

01:30 S minus 10 plus 1.

01:33 All right.

01:34 So s squared plus 2s plus 8.

01:38 Y equals minus s plus 9.

01:44 So y is minus s plus 9 over s squared plus 2s plus 8.

01:55 Okay, so now what are we going to do? b squared for...

02:22 I'm going to, i think, work on the bottom.

02:25 I think i'm going to complete the square there.

02:28 I'm going to add one and subtract.

02:31 One so i get s plus 1 squared plus 7 and so then on the top i need that minus s plus 9 to be in terms of s plus 1 so i can do this last thing to it so minus s plus 9 is minus okay i'm just going to make it s plus 1.

03:00 So what i did there was subtracted 1.

03:05 So i need to add one.

03:12 So this is the same thing as minus s plus 1 plus 10 over s plus 1 square plus 7 or minus s plus 1 over s plus 1 square plus 7 plus 10 s plus 1 square plus 7.

03:36 Okay, sorry.

03:38 Okay.

03:39 So so now i'm going to inverse transform...

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