Laplace transform by partial equation
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D
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If I were to do this problem, I would start with LT of y" and y'.
What do you get?
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i already solve the differential equation and now i stuck, how to find the Laplace transform
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D
Deleted member 4993
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Through Laplace transform technique you found that
y(s) = (s^2 + 10s + 5)/(s*(s^2+6s+13)). To calculate the "inverse transform" assume:
(s^2 + 10s + 5)/(s*(s^2+6s+13)) = A/s + (Bs + C)/(s^2+6s+13)
You need to solve for A, B & C
I'll start you off by solving for A.
(s^2 + 10s + 5)/(s*(s^2+6s+13)) = A/s + (Bs + C)/(s^2+6s+13)
Multiply by s (both sides of the equation)
s*(s^2 + 10s + 5)/(s*(s^2+6s+13)) = A + (Bs^2 + Cs)/(s^2+6s+13)
(s^2 + 10s + 5)/(s^2+6s+13) = A + (Bs^2 + Cs)/(s^2+6s+13)
The above relation is true for every value of s.
When s=0,
(0^2 + 10*0 + 5)/(0^2+6*0+13) = A + (B*0^2 + C*0)/(0^2+6*0+13)
5/13 = A
Now solve for B and C..........
If you are not sure - how to proceed - do some google search with key-word:
"partial fraction decomposition"
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D
Deleted member 4993
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Do you have a table for Laplace Transforms?
You will have to rewrite the denominator in the form of:
(s + M)2 + N2
using the technique of completing the square.
Use: https://www.dartmouth.edu/~sullivan/22files/New Laplace Transform Table.pdf
Look at the entry#26
okay i get it ..thank you very much