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Thread: solve this equation for

  1. #1
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    solve this equation for

    How to solve this equation for x ??

    A sin (x − B)=exp Cx

    Where A,B, C ...are constants
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  2. #2
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    Re: solve this equation for

    You have asked: How to solve this equation for x ??

    Since no-one else has attempted a reply, I will.
    What follows is a 'starter', which hopefully you will be able to complete.

    Equations like this will have an infinity of solutions, usually expressed as a power series.
    My attempt is based on that idea . . .

    Consider the trig. identity:
    a.sinx - b.cosx = √(aČ + bČ).sin(x - α), where tanα = b/a and is 1st. quadrant.

    For this Q., let √(aČ + bČ) = A; α = B.
    Then we now have:
    a.sinx - b.cosx - e^(cx).

    Using the power series for sinx, we obtain:
    a.sinx = a[x - x^2/2! + x^4/4! + . . . .]

    and similarly for cosx:
    b.cosx = b[x - x^3/3! + x^5/5! - . . . .]

    and for e^cx:
    e^cx = 1 + cx + (cx)^2/2! + (cx)^3/3! + . . . .

    Hence, we finally arrive at:
    a[x - x^2/2! + x^4/4! + . . . .] - b[x - x^3/3! + x^5/5! - . . . .] = 1 + cx + (cx)^2/2! + (cx)^3/3! + . . . .

    I'll leave the rest up to you (I did say that what follows is a 'starter' ).

    Hint: next: move the RHS to the LHS (changing signs accordingly) and simplify the result.
    An infinite power series will be produced.
    Hopefully, you can take things from there . . . .

    Hope that helps!

    Al. / Skywave
    June 18, 2017
    Last edited by Skywave; Jun 18th 2017 at 10:24 AM.
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  3. #3
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    Re: solve this equation for

    This individual posted more than once with variations on the theme of this particular post ...

    Find out solution

    ... which is probably why no one bothered to respond to this one.
    Thanks from romsek
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  4. #4
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    Re: solve this equation for

    Skeeter: "This individual posted more than once with variations on the theme of this particular post."

    I didn't know that. Moreover, did I not read somewhere that doing suchlike (posting same Q. more than once) is against a Forum rule?

    Al.
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  5. #5
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    Re: solve this equation for

    Forum Rules

    rule #10
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  6. #6
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    Re: solve this equation for

    Ah! Yes! Rule 10: I knew I had read that somewhere.
    But, being a newcomer here, might I respectfully ask that if that duplication had been spotted by a moderator, why was that duplicate post not deleted?

    Al.
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  7. #7
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    Re: solve this equation for

    Because we only have one moderator, topsquark ... the site administrator has not authorized additional moderators for whatever reason(s) since he took over this site years ago. Suffice to say, it is what it is & we deal with it.
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  8. #8
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    Re: solve this equation for

    Thank you, Skeeter: all understood. I've nothing else to add nor to enquire about.

    Regards,
    Al.
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