Can someone plaese check and correct this problem if there are errors? Thanks So

Question

Can someone plaese check and correct this problem if there are errors? Thanks
Solve y"-5y'-6y=e^(-2t) where y’(0) = 1 and y(0) = -1 using LaPlace Transforms

1. Step 1: Rewrite the left side of the equation using the LaPlace substitutions for y”, y’, and y.
Y” = s^2 L(s)+2s-1
Y’ =5sL(s)+5
Y = 6L(s)

Left Side of give equation = s^2 L(s)+2s-1-5(sL(s)+5)-6L(s)

2. Step 2: Transform the right side of the equation using the appropriate LaPlace Transform.
Which transform matches the right side of the given equation?
The transform is 3 = 1/(s+a)
e^(-2t)= e^(-at)=1/(s+2)
3. Step 3: Solve the equation resulting from steps 1 and 2 for L(y). What steps must you take to accomplish this? In what order should you take them?

L(y)=1/((s+2)(s+1)(s-6))+5s/((s+1)(s-6))+6/((s+1)(s-6))

4. Step 4: Use inverse transforms to rewrite the result of step 3 back into y(t) form.

L(y)=1/((s+2)(s+1)(s-6))+5s/((s+1)(s-6))+6/((s+1)(s-6))

Break this down into smaller pieces.
Which transform matches 5s/((s+1)(s-6))? Hint: You may need to rewrite the expression to get an exact match.
The transform is 10 = (s(a-b))/((s+a)(s-b))

5s/((s+1)(s-6)) =-5/7 e^(-t)-30/7 e^6t

Which transform matches 6/((s+1)(s-6))? Hint: You may need to rewrite the expression to get an exact match.
The transform is 9 = (b-a)/((s+a)(s-b))
6/((s+1)(s-6))=
There is no transform that matches 1/((s+2)(s+1)(s-6)). How will we transform it back to y(t)? Hint: Use the Partial Fraction Decomposition.
A/(s+2)+B/(s+1)+C/(s-6)=1/((s+2)(s+1)(s-6))

One you determine what A, B, and C what transform will you use the turn A/(s+2)+B/(s+1)+C/(s-6) into y(t) form?
Transform 1 = 1/s

A/(s+2)+B/(s+1)+C/(s-6)=(1/8)/(s+2)-(1/7)/(s+1)+(1/56)/(s-6)

Explanation / Answer

If you scroll down on your Lab in step 5 it gives you the final answers to all of the above questions. you just need to show a little work and you should be good.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.