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melmel
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linear D.E of nth order with constant coefficient...help guys
.
 10 months ago
 10 months ago
melmel Group Title
linear D.E of nth order with constant coefficient...help guys .
 10 months ago
 10 months ago

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melmel Group TitleBest ResponseYou've already chosen the best response.0
dw:1381226444353:dw
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
This WILL be messy... are you up for it? :D
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
For these kinds of differential equations, the general form of the solution is given by \[\Large f^{(h)}(x) + f^{(p)}(x)\] where the f^h is the general solution to the homogeneous equation while f^p is any particular solution of this equation. Can you find the general solution to the homogeneous equation?
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
\[m ^{^{2}}=11\]
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
What does that mean? D:
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
\[y=e ^{a}\]
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Oh wait... there's no y' term?
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
get the higher order first D.E
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
So basically, it's \[\Large y''  11y = xe^x\]?
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
\[m ^{2} +1 12 =0\]
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
then m= square root of 11
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
then get the vlue of y
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
\[y=C{1}^{+\sqrt{11}x}+C{2}^{\sqrt{11}x}\]
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
Im right? what is the next get the other y which from Xe^x
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
whic is y= Ae^u
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
take derivative until second derivative
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
ang get the value of A I stocked here
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
help guys if Im wrong :(
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Well, if it doesn't work with only one undetermined coefficient, did you try 2? Specifically this: \[\Large y = \color{blue}Axe^x + \color{red}Be^x\]
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
subst the value of Y" ,Y' and Y to the y′′+ y 12y
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
where did you get this y=Axex+Bex
 10 months ago

melmel Group TitleBest ResponseYou've already chosen the best response.0
@UnkleRhaukus
 10 months ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
are you sure the second term in the question isn't a derivative?
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Odd, isn't it :D
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Oh by the way, I didn't actually "get" that Axe^x + Be^x, for all intents and purposes, it IS just a guess... see if it gets you the coefficients you want, since Axe^x alone doesn't seem to do it.
 10 months ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
if not (yes strange), then i think you (@melmel ) got the complementary homogenous solution \[\large f^h(x)=y_c(x)=C_{1}e^{+\sqrt{11}x}+C_{2}e^{\sqrt{11}x}\] {forgot to type the e's in the bases }
 10 months ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
Which method to calculate the particular solution \[f^h(x)=y_p(x)\] are you going to use; undetermined coefficients, operator D , or variation of parameters, @melmel ?
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
apparently offline :( Oh well, onwards and upwards XD
 10 months ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
^_^ thanks
 10 months ago
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