# de-t2(1) - NAME TEST2/MAP2302 Page 1 of 4 General...

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NAME: TEST2/MAP2302 Page 1 of 4 ______________________________________________________________________ General directions: Show all essential work very neatly. Use correct notation when presenting your computations and arguments. Write using complete sentences. Be careful. Since the answer really consists of all the magic transformations, do not "box" your final results. Communicate. Eschew Obfuscation. Show me all the magic on the page. ______________________________________________________________________ 1. (30 pts.) Obtain the general solution to each of the following linear homogeneous constant coefficient equations. (a) (b) (c) ______________________________________________________________________ 2. (10 pts.) Find the unique solution to the initial value problem given that a fundamental set of solutions to the corresponding homogeneous equation is { 1, e x } and a particular integral of the original ODE is Hint: Save time. Use the stuff served on the platter with the cherry on top.

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TEST2/MAP2302 Page 2 of 4 ______________________________________________________________________ 3. (15 pts.) Find a particular integral, y p , of the differential equation Do not write the general solution. ______________________________________________________________________ 4. (10 pts.) Set up the correct linear combination of undetermined coefficient functions you would use to find a
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