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Math Help - Differentials

  1. #1
    IBD
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    Differentials

    Hi guys! I ve got this very difficult exercise for my uni. Could someone please help? Thank you in advance.

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  2. #2
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    Quote Originally Posted by IBD View Post
    Hi guys! I ve got this very difficult exercise for my uni. Could someone please help? Thank you in advance.

    What's the exercise?
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  3. #3
    IBD
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    Thanks for looking into my problem Prove It. I have inserted a picture of the exercise but it seems that you could not see it. I have now uploaded it as an attachment. Thanks again
    Attached Thumbnails Attached Thumbnails Differentials-rsz_exercise2.jpg  
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  4. #4
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    Why not substitute D and S into the equation for p''?

    This will give you a second order constand coefficient ODE.
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  5. #5
    IBD
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    Thanks Prove it for your response. I will substitute into p'' however i don't get p' this way. could you please let me know how i will obtain the differential equation that the first question asks for?
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    Quote Originally Posted by IBD View Post
    Thanks Prove it for your response. I will substitute into p'' however i don't get p' this way. could you please let me know how i will obtain the differential equation that the first question asks for?
    You should end up with

    p''(t) = a[d_0 + d_1p(t) - (s_0 + s_1p(t))]

     = ad_0 + ad_1p(t) - as_0 - as_1p(t)

     = (ad_1 - as_1)p(t) + ad_0 - as_0.


    So p''(t) + (as_1 - ad_1)p(t) = ad_0 - as_0.


    Solve the homogeneous characteristic equation:

    m^2 + as_1 - ad_1 = 0

    m^2 = ad_1 - as_1

    m^2 = a(d_1 - s_1).


    Now since d_1 < 0 and s_1 > 0, this means d_1 - s_1 < 0.

    Also, since a > 0, this means a(d_1 - s_1) < 0.


    So you have m^2 equaling a negative number. What does this tell you about m? Can you solve the DE now?
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  7. #7
    IBD
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    My dearest Prove It can you please send me a pm with some contact information (email)? I cannot send you a pm because I am a new member and don't have 15 posts. I need to discuss something in private. Thanks
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