Differential Equation, Rewriting solution

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SUMMARY

The discussion focuses on rewriting a solution to a differential equation involving the expression ejθ = cos(θ) + jsin(θ). The user seeks assistance in combining constants A and B into a single term, indicating a lack of familiarity with solving differential equations. A suggestion is made to utilize the trigonometric identity for the cosine of the sum of two angles to aid in the solution process. The conversation highlights the importance of understanding trigonometric identities in solving differential equations.

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  • Familiarity with complex numbers and Euler's formula
  • Knowledge of trigonometric identities, specifically the cosine of the sum of two angles
  • Basic algebra skills for manipulating equations
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  • Study the method of solving second-order differential equations
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  • Explore trigonometric identities relevant to angle addition
  • Practice rewriting expressions involving constants in differential equations
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Students studying differential equations, mathematics enthusiasts, and anyone seeking to improve their understanding of complex numbers and trigonometric identities.

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



ejθ = 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
 

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