Differential Equation, Rewriting solution

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The discussion revolves around rewriting a solution to a differential equation and expressing constants C and alpha as functions of A and B. The user is struggling to combine terms due to the presence of constants A and B. They have completed the first part of the homework but did so incorrectly, lacking understanding of how to solve differential equations. Participants suggest using trigonometric identities to assist in the solution process. The conversation emphasizes the need for foundational knowledge in solving differential equations and applying trigonometric concepts.
ecoo
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Homework Statement



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(also express C and alpha as functions of A and B)

I need help with the second part (rewriting the solution).

Homework Equations



e = cos(θ) + jsin(θ)

The Attempt at a Solution



Unfortunately, I can't think of how to even begin solving. I have the notion that I have to combine the two terms into one, however the A and B constants prevent me from doing so. Can someone point me in the right direction?

Thanks
 

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Have you been able to do the first part?
 
Chestermiller said:
Have you been able to do the first part?

Yes, I have already done the first part. I did do it backwards, however, because I do not know how to solve differential equations (second derivative ---> function) yet.
 
ecoo said:
Yes, I have already done the first part. I did do it backwards, however, because I do not know how to solve differential equations (second derivative ---> function) yet.
Then by the same backwards approach, do you know the trigonometric identity for the cosine of the sum of two angles?
 
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Chestermiller said:
Then by the same backwards approach, do you know the trigonometric identity for the cosine of the sum of two angles?

Thanks for the help
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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