- #1
iismitch55
- 11
- 0
23.) y'' + 2y' + y = 4e-t; y(0) = 2, y'(0) = -1
Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as2 + bs + c)
My attempt:
a = 1, b = 2, c = 1
F(s) = 4 L{ e-t } = 4/(s+1) (From Laplace Transform Table)
Plugging and simplifying:
Y(s) = (2s2 + 5s + 7)/[(s + 1)(s2 + 2s + 1)
Here is where I get stuck. I've tried Partial Fraction Decomposition a couple times, with no real luck. The numerator also doesn't factor. I need to get it to match something in my table (sorry I have no way to post it). I do find it peculiar that the denominator is a perfect cube. Any help would be greatly appreciated!
Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as2 + bs + c)
My attempt:
a = 1, b = 2, c = 1
F(s) = 4 L{ e-t } = 4/(s+1) (From Laplace Transform Table)
Plugging and simplifying:
Y(s) = (2s2 + 5s + 7)/[(s + 1)(s2 + 2s + 1)
Here is where I get stuck. I've tried Partial Fraction Decomposition a couple times, with no real luck. The numerator also doesn't factor. I need to get it to match something in my table (sorry I have no way to post it). I do find it peculiar that the denominator is a perfect cube. Any help would be greatly appreciated!