# 4th order homogeneous linear ODE with constant coefficients

1. Aug 4, 2009

### 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.

2. Aug 4, 2009

### Newtime

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.

3. Aug 5, 2009

### 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.

4. Apr 18, 2010

### omarxx84

Re: 4th order homogeneous linear ODE with variable coefficients

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...........

5. Apr 18, 2010

### omarxx84

Re: 4th order homogeneous linear ODE with variable coefficients

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...........

6. Apr 20, 2010

### omarxx84

7. Apr 20, 2010

### omarxx84

8. Apr 25, 2010

### 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.

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9. Apr 25, 2010

### 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 seperation 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...

10. Apr 25, 2010

### Nick Bruno

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

11. May 11, 2010

### 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...

12. May 11, 2010

### Redbelly98

Staff Emeritus

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.

Last edited by a moderator: May 4, 2017
13. May 12, 2010

### 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..

14. May 13, 2010

### 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.