2930 P1.pdf - 1a Solve the initial value problem ty(t 1 y...

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1a Solve the initial value problem ( 1) t ty t y e  , 0 t , ( ) y a (15pts) 1b. How do solutions behave as 0 t (from the positive side) ? How does the behavior depend on the choice of initial value a ? (5pts) Let 0 a be the initial value for which the transition from one type of behavior to another occurs. Find 0 a . (5pts)
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2a. Find the solution of the initial value problem 2 / / du dx u x ,   1/ 3 u e (where e is Euler’s number = 2.71828… ). (13pts) 2b. Plot the graph of the solution and determine the interval in which the solution is defined. (12pts)
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3a. Solve the initial value problem 2 9 1 / 4 x y dy dx y x , (1) 0 y (15pts) 3b. Find the general solution of 1 3 / / 2 / 2 dy dx y x y x , 0 x (10pts)
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4 Consider the differential equation / ( ) dy dt
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