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

http://img2.immage.de/200270494rszexercise2.jpg

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- Feb 20th 2010, 12:43 AMIBDDifferentials
Hi guys! I ve got this very difficult exercise for my uni. Could someone please help? Thank you in advance.

http://img2.immage.de/200270494rszexercise2.jpg - Feb 20th 2010, 01:02 AMProve It
- Feb 20th 2010, 01:11 AMIBD
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

- Feb 20th 2010, 01:39 AMProve It
Why not substitute D and S into the equation for $\displaystyle p''$?

This will give you a second order constand coefficient ODE. - Feb 20th 2010, 09:16 PMIBD
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?

- Feb 20th 2010, 09:31 PMProve It
You should end up with

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

$\displaystyle = ad_0 + ad_1p(t) - as_0 - as_1p(t)$

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

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

Solve the homogeneous characteristic equation:

$\displaystyle m^2 + as_1 - ad_1 = 0$

$\displaystyle m^2 = ad_1 - as_1$

$\displaystyle m^2 = a(d_1 - s_1)$.

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

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

So you have $\displaystyle m^2$ equaling a negative number. What does this tell you about $\displaystyle m$? Can you solve the DE now? - Feb 20th 2010, 11:30 PMIBD
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