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1. Find the general solution y(t) of the ordinary di erential equation
where ω is a non-negative constant. (Consider the ω = 0 and ω > 0 cases separately).
2. Use Laplace transform to solve the following di erential equation for y(t):
given that y(0) = 0 and y'(0) = 2.3. Consider the following partial di erential equation for u(x; t)
(a) If is a function of t, derive two ODEs by separation of variables.
(b) If is a function of x, derive two ODEs by separation of variables.
Q. If the output signal fromanAMmodulator is given by u(t) = 5 cos 1800 πt + 20 cos 2000 πt + 5 cos 2200 πt , determine: (a) The modulating signal m(t) and carrier c(t). (b)
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