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ChmEBest 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?
 one year ago

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

acrossBest 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.
 one year ago

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

ChmEBest ResponseYou've already chosen the best response.0
That makes sense I'm going to look that up. Thanks
 one year ago

ChmEBest ResponseYou've already chosen the best response.0
@across I found it you are right
 one year ago

ChmEBest 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
 one year ago

ChmEBest ResponseYou've already chosen the best response.0
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.
 one year ago

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

ChmEBest ResponseYou've already chosen the best response.0
@Directrix @Hero Can I have a little push in the right direction
 one year ago

ChmEBest 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?
 one year ago

HeroBest ResponseYou've already chosen the best response.0
Sorry, I'm busy doing my own work at the moment.
 one year ago

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

ChmEBest 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?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
where are you up to
 one year ago

ChmEBest 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
 one year ago

ChmEBest ResponseYou've already chosen the best response.0
I feel like I have my roots and s correct
 one year ago

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

ChmEBest 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
 one year ago

ChmEBest 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.
 one year ago

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

ChmEBest 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
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
its a second order equation there will be two solutions
 one year ago

ChmEBest ResponseYou've already chosen the best response.0
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
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
take the first and second derivative of y_p
 one year ago

ChmEBest 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
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
see you next time
 one year ago
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