melmel
linear D.E of nth order with constant coefficient...help guys
.
Delete
Share
This Question is Open
melmel
Best Response
You've already chosen the best response.
0
|dw:1381226444353:dw|
terenzreignz
Best Response
You've already chosen the best response.
1
This WILL be messy... are you up for it? :D
melmel
Best Response
You've already chosen the best response.
0
yes
terenzreignz
Best Response
You'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?
melmel
Best Response
You've already chosen the best response.
0
\[m ^{^{2}}=11\]
terenzreignz
Best Response
You've already chosen the best response.
1
What does that mean? D:
melmel
Best Response
You've already chosen the best response.
0
\[y=e ^{a}\]
terenzreignz
Best Response
You've already chosen the best response.
1
Oh wait... there's no y' term?
melmel
Best Response
You've already chosen the best response.
0
get the higher order first D.E
terenzreignz
Best Response
You've already chosen the best response.
1
So basically, it's
\[\Large y'' - 11y = xe^x\]?
melmel
Best Response
You've already chosen the best response.
0
\[m ^{2} +1 -12 =0\]
melmel
Best Response
You've already chosen the best response.
0
then m= square root of 11
melmel
Best Response
You've already chosen the best response.
0
then get the vlue of y
melmel
Best Response
You've already chosen the best response.
0
\[y=C{1}^{+\sqrt{11}x}+C{2}^{-\sqrt{11}x}\]
melmel
Best Response
You've already chosen the best response.
0
Im right? what is the next get the other y which from Xe^x
melmel
Best Response
You've already chosen the best response.
0
whic is y= Ae^u
melmel
Best Response
You've already chosen the best response.
0
take derivative until second derivative
melmel
Best Response
You've already chosen the best response.
0
ang get the value of A I stocked here
melmel
Best Response
You've already chosen the best response.
0
help guys if Im wrong :(
terenzreignz
Best Response
You've already chosen the best response.
1
Well, if it doesn't work with only one undetermined coefficient, did you try 2?
Specifically this:
\[\Large y = \color{blue}Axe^x + \color{red}Be^x\]
melmel
Best Response
You've already chosen the best response.
0
subst the value of Y" ,Y' and Y to the y′′+ y -12y
melmel
Best Response
You've already chosen the best response.
0
where did you get this y=Axex+Bex
melmel
Best Response
You've already chosen the best response.
0
@UnkleRhaukus
UnkleRhaukus
Best Response
You've already chosen the best response.
1
are you sure the second term in the question isn't a derivative?
terenzreignz
Best Response
You've already chosen the best response.
1
Odd, isn't it :D
terenzreignz
Best Response
You'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.
UnkleRhaukus
Best Response
You'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 }
UnkleRhaukus
Best Response
You'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 ?
terenzreignz
Best Response
You've already chosen the best response.
1
apparently offline :(
Oh well, onwards and upwards XD
terenzreignz
Best Response
You've already chosen the best response.
1
^_^
thanks