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ChmE
 2 years ago
Method of undetermined coefficients...
ChmE
 2 years ago
Method of undetermined coefficients...

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ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0Must 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?

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0Find a particular solution to the differential equation\[4y''+11y'3y=2te ^{3t}\]

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

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

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0That makes sense I'm going to look that up. Thanks

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0@across I found it you are right

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

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0Ok @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.

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0\[Y _{p}= t(Ae ^{3t})\]Do I have to include the other root as well?

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0@Directrix @Hero Can I have a little push in the right direction

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0@Hero do you see a mistake I have made or is anything coming to you about what to do next?

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

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

ChmE
 2 years ago
Best 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?

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

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0I 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

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

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

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0Oh 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

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

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

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0Why 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
 2 years ago
Best ResponseYou've already chosen the best response.0its a second order equation there will be two solutions

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0So 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
 2 years ago
Best ResponseYou've already chosen the best response.0take the first and second derivative of y_p

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