4th order homogeneous linear ODE with constant coefficients

[mappleby15]

Can someone explain to to me how to find the general solution of the fourth order ODE

y''''-y''=0

Right now I have

y(x)=a+b*x+c*e^-x+d*e^x

where a,b,c and d are constants.

Not sure if this is correct just wanted to double check.

 

[Newtime]

Can someone explain to to me how to find the general solution of the fourth order ODE

y''''-y''=0

Right now I have

y(x)=a+b*x+c*e^-x+d*e^x

where a,b,c and d are constants.

Not sure if this is correct just wanted to double check.

Seems right to me at first glance. Your r values for the aux. eq. are correct and that's about all the problem comes down to since it is set equal to 0 and not a constant or another function which would lead to undetermined coefficients.

 

[Mute]

Yes, it's correct. Another way you can check is to note that if you set u = y'', you get

u'' - u = 0,

an equation which you pressumably know the solution to. It's then just a matter of integrating twice.

 

[omarxx84]

please. anyone can help me to get the general solution of the equation:
EI(X)Ø'''(X)+Km(x)Ø(x)=0
where: k= constant
EI(X) and m(x) are variable coefficients
and i will be very grateful for him...

 

[omarxx84]

please. anyone can help me to get the general solution of the equation:
EI(X)Ø'''(X)+Km(x)Ø(x)=0
where: k= constant
EI(X) and m(x) are variable coefficients
and i will be very grateful for him...

 

[omarxx84]

my colleages...why i didnot answer about my question?

 

[omarxx84]

sorry, why i didnot find any answer about my question??

 

[Nick Bruno]

this may help you. Its something i made for the 1d 4th order wave eqn... i think you will find pg 7 handy.

 

[omarxx84]

thank you very much Nick Bruno...But the problem is that, how can find the solution of the equation when EI and m are variable with x-axis and not constants...i think that the equation can be solved by separation of variables but the resulted equations will be on the form of ODEs with variable coefficients which i am looking for their solutions, and i will be thankful for anybody can help me in this subject...

 

[Nick Bruno]

looks like you may need to use sturm-liouville and use a computer to solve your problem.

 

[omarxx84]

Hi colleages, can anyone help me to get this paper which is entitled;"solution of ordinary linear differential equations with variable coefficients by impulsive admittances". this paper in the quarterly journal of mechanics and applied mathematics, volume 6, no.1, pp.122-127. by W.J. Duncan, 1953...please help me to get this paper and i will be very grateful for this...

 

[Redbelly98]

Moderator's note: please ask new questions by creating and posting in a new thread, rather than posting in existing threads. New threads can be created by clicking the "New Topic" [PLAIN]https://www.physicsforums.com/Prime/buttons/newthread.gif button.

You can purchase the paper here:
http://qjmam.oxfordjournals.org/cgi/reprint/6/1/122

If you don't want to spend 32 $US, I would look for the journal at the math department library of a local university.

 

[omarxx84]

my colleage...i havenot the way to buy this paper, because, i havenot the prepay cards...
please, if you can to get this paper,send it to me..

 

[HallsofIvy]

Omarxx84, you are coming awfully close to being banned from this forum.

First, you "hijacked" someone else's thread to ask a completely unrelated question which is very rude. (It's not that hard to click on the "new topic" button on the main menu.)

Second, you are asking people to send you a copy of a copy-righted paper, which is a crime.