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de-t1-a - NAME Very Brief Answers[Em Tiodi TEST1/MAP2302...

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NAME: Very Brief Answers [Em Tiodi] TEST1/MAP2302 Page 1 of 3 ______________________________________________________________________ General directions: Read each problem carefully and do exactly what is requested. Full credit will be awarded only if you show all your work neatly, and it is correct. Write complete sentences, and use notation correctly. What is illegible or incomprehensible is worthless. Since the answer really consists of all the magic transformations, do not box your final result. Show me all the magic on the page. Communicate. Eschew obfuscation. _________________________________________________________________ 1. (80 pts.) Solve each of the following differential equations or initial value problems. If there is no initial condition, obtain the general solution. [20 points/part] (a) The ODE is obviously separable. dy dx 5 x 4 cos 2 ( y ) ; y (0) π 3 . There are infinitely many constant solutions to the ODE from the zeros of cos( y ): y ( x ) = ( π /2)(2 k +1), k any integer. None is a solution to the IVP. Separating variables and applying the initial conditions yields: , an implicit solution, or better , and explicit solution alive and well on the whole real line.
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