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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.
The circuit below will be most efficiently analyzed by obtaining the Thevenin equivalent circuit for the circuit to the left of the points (a-b) on the schematic. The capacitor is
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