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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.
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(a) Now consider a typical open-wire transmission line with parameters of R = 14 /mi, L = 4.6 mH/mi, C = 0.01 µF/mi, and G = 0.3×10 -6 S/mi. If the line operates at 1 kHz, find t
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