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Function and Differential Equations

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Please assist me with the attached problems relating to functions and (partial) differential equations. Thanks very much.

Please tell me which is true and which is false. Then please explain why it is true or false. As you see c, d, and e are the answers I believe and next to some in parenthesis are some basic explanations. I need to understand why these are the answers and how you get the answers. Please make simple to understand.

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Solution Summary

The functions and differential equations are given.

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