anonymous
  • anonymous
Method of undetermined coefficients...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Must be in the form\[ay''+by'+cy=Ct ^{m}e ^{rt}\]What does C stand for? I thought it was a constant but the equation\[y''+2y'-y=t ^{-1}e ^{t}\]Does not satisfy this method. i assumed C=1 so it would, bu tit doesn't. Explanation?
anonymous
  • anonymous
@UnkleRhaukus
anonymous
  • anonymous
Find a particular solution to the differential equation\[4y''+11y'-3y=-2te ^{-3t}\]

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across
  • across
I believe that the method only applies for \(m\geq0\), but I cannot recall to save my life.
anonymous
  • anonymous
\[4r ^{2}+11r-3=0\rightarrow (4r-1)(r+3)\rightarrow r= \frac{ 1 }{ 4 },-3\]
anonymous
  • anonymous
That makes sense I'm going to look that up. Thanks
anonymous
  • anonymous
@across I found it you are right
anonymous
  • anonymous
since -3 does appear as a root s=1 which is the multiplicity of the root -3
anonymous
  • anonymous
Ok @UnkleRhaukus I could use a little help on my last problem of the night. I posted the question in this stream 3rd from the top.
anonymous
  • anonymous
\[Y _{p}= t(Ae ^{-3t})\]Do I have to include the other root as well?
anonymous
  • anonymous
@Directrix @Hero Can I have a little push in the right direction
anonymous
  • anonymous
@Hero do you see a mistake I have made or is anything coming to you about what to do next?
Hero
  • Hero
Sorry, I'm busy doing my own work at the moment.
anonymous
  • anonymous
The answer in the back of the book is \[(\frac{ t }{ 13 }-\frac{ 8 }{ 169 })te ^{-3t}\]
anonymous
  • anonymous
Oh, I understand
anonymous
  • anonymous
@satellite73 @.Sam.
anonymous
  • anonymous
@UnkleRhaukus Just in time I was about to give up. Do you mind helping me with this last question?
UnkleRhaukus
  • UnkleRhaukus
where are you up to
anonymous
  • anonymous
I feel like I need to plug in \[Y _{p},Y'_{p}, Y''_{p}\]into the original to solve for A. I am up to writing an equation for Yp
anonymous
  • anonymous
I feel like I have my roots and s correct
UnkleRhaukus
  • UnkleRhaukus
\[4y''+11y'-3y=-2te ^{-3t}\] \[4r^2+11r-3=0\]\[(4r-1)(r+3)=0\]\[r=1/4,-3\] \[y_c=ae^{t/4}+be^{-3t}\]
anonymous
  • anonymous
Oh ya I forgot, when you have two diff roots you need to use two different unknowns. What about the t^s? My teacher threatened us if we forgot that on the test
anonymous
  • anonymous
As i understand it t^s, where s is the multiplicity of your roots needs to be out in front.
UnkleRhaukus
  • UnkleRhaukus
\[y_p=t\left(c\cdot e^{-3t}+d\cdot t\cdot e^{-3t}\right)\]
anonymous
  • anonymous
Why do you have two terms in the ( ) if m=1 shouldn't there be 1. And I don't mean to come across like I'm questioning you, just trying to undersstand
UnkleRhaukus
  • UnkleRhaukus
its a second order equation there will be two solutions
anonymous
  • anonymous
So I see your Yp matches the books except I need to now solve for c and d by plugging Yp into the original equation right?.........Ok
UnkleRhaukus
  • UnkleRhaukus
take the first and second derivative of y_p
anonymous
  • anonymous
Right then plug it in. I can do that on my own later. Thanks for your help again. I'm calling it a night
UnkleRhaukus
  • UnkleRhaukus
see you next time

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