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ChmE Group TitleBest ResponseYou've already chosen the best response.0
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?
 2 years ago

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Find a particular solution to the differential equation\[4y''+11y'3y=2te ^{3t}\]
 2 years ago

across Group TitleBest ResponseYou've already chosen the best response.1
I believe that the method only applies for \(m\geq0\), but I cannot recall to save my life.
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
\[4r ^{2}+11r3=0\rightarrow (4r1)(r+3)\rightarrow r= \frac{ 1 }{ 4 },3\]
 2 years ago

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That makes sense I'm going to look that up. Thanks
 2 years ago

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@across I found it you are right
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
since 3 does appear as a root s=1 which is the multiplicity of the root 3
 2 years ago

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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.
 2 years ago

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\[Y _{p}= t(Ae ^{3t})\]Do I have to include the other root as well?
 2 years ago

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@Directrix @Hero Can I have a little push in the right direction
 2 years ago

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@Hero do you see a mistake I have made or is anything coming to you about what to do next?
 2 years ago

Hero Group TitleBest ResponseYou've already chosen the best response.0
Sorry, I'm busy doing my own work at the moment.
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
The answer in the back of the book is \[(\frac{ t }{ 13 }\frac{ 8 }{ 169 })te ^{3t}\]
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
Oh, I understand
 2 years ago

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@satellite73 @.Sam.
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
@UnkleRhaukus Just in time I was about to give up. Do you mind helping me with this last question?
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
where are you up to
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
I feel like I have my roots and s correct
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
\[4y''+11y'3y=2te ^{3t}\] \[4r^2+11r3=0\]\[(4r1)(r+3)=0\]\[r=1/4,3\] \[y_c=ae^{t/4}+be^{3t}\]
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
As i understand it t^s, where s is the multiplicity of your roots needs to be out in front.
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
\[y_p=t\left(c\cdot e^{3t}+d\cdot t\cdot e^{3t}\right)\]
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
its a second order equation there will be two solutions
 2 years ago

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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
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
take the first and second derivative of y_p
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.0
Right then plug it in. I can do that on my own later. Thanks for your help again. I'm calling it a night
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
see you next time
 2 years ago
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