Originally Posted by
Davidc2233 Hello
I wonder if you can help? I believe I'm doing this correctly, but iv got caught up in the algebra. Ill list all the question and then as far as I have got.
Kind regards
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You are required to solve the following differential equation by the Laplace transform method:
d^2x/dt^2 + 5*dx/dt - 24x = 4t
with
x(0) = 2
x'(0)=9
(i)
Take the Laplace transform of the differential equation and solve the resulting equation for X, the Laplace transform of the solution
Give your answer as a function of only. Omit the "X ="
d^2x/dt^2 + 5*dx/dt - 24x = 4t
Taking the Laplace transform
L(d^2x/dt^2) + 5L(dx/dt) -24L (x) = 4L(t)
(s^2X - sx(0)-x'(0)) + 5( sX - x(0)) - 24X = 4/s^2
Sub in values given within questions for x(0) and x'(0)
(s^2X - 2s - 9) + (5sX - 10) - 24X = 4/s^2
Expanding brackets out and collecting like terms
X(s^2+5s-24) = 4/s^2 + 2s +19
Factorising LHS
X((s-3)(s+8)) = 4/s^2 + 2s +19
I can't see where to go next to, iv looked at brining the (s-3)(s+8) to the RHS but I get muddled with all the numbers and it doesn't seem to look correct.
Thanks again