Differential Equation, Rewriting solution

In summary, the conversation is about rewriting a solution for a problem involving the expression ejθ = cos(θ) + jsin(θ) as a function of A and B. The person is struggling with the second part and is asking for help. They have already completed the first part and are using a backwards approach, but are unsure of how to solve differential equations. The conversation ends with a question about the trigonometric identity for the cosine of the sum of two angles.
  • #1
ecoo
86
2

Homework Statement



Untitled.png


(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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  • #2
Have you been able to do the first part?
 
  • #3
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.
 
  • #4
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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Likes ecoo
  • #5
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
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model many physical and natural phenomena, such as the motion of objects, the growth of populations, and the flow of fluids.

2. Why do we need to rewrite solutions to differential equations?

Rewriting solutions to differential equations can make them easier to understand and solve. It allows us to manipulate the equation into a form that is more useful for our specific problem or application.

3. What are some common techniques for rewriting solutions to differential equations?

Some common techniques for rewriting solutions to differential equations include separation of variables, substitution, and integrating factors. These techniques help to simplify the equation and make it easier to solve.

4. Can all differential equations be rewritten?

No, not all differential equations can be rewritten. Some equations are already in their simplest form and cannot be simplified any further. Others may require more advanced mathematical techniques to rewrite them.

5. How can rewriting solutions to differential equations help in real-world applications?

Rewriting solutions to differential equations allows us to model and understand real-world phenomena more accurately. It can help us make predictions and solve problems in fields such as physics, engineering, and economics.

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