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Unformatted text preview: y + p ( t ) y = c 1 g ( t ) , y ( t ) = c 2 . 3 3. [20%] Suppose that a , b are constants. Find the general solution of y + ay = b. If a > 0, how does the solution behave as t → + ∞ ? 4 4. [20%] (a) Find the solution of the initial value problem ty + 3 y = 1 t , t > , y (1) = y . (b) For what initial values y is the solution y ( t ) equal to zero for some t > 0? 5 5. [20%] (a) Solve the initial value problem ty + y 2 = 0 , y (1) = 1 . (b) What is the largest tinterval in which the solution exists? 6 6. [20%] Consider the ODE y = y 2y 4 . (a) Find all equilibrium solutions. (b) Sketch the phase line. (c) Determine the stability of the equilibria you found in (a). 7...
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 Spring '08
 Hunter
 Equations, ........., 10%, 20%, ty

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