Hey MHF,

I got stuck on finding the gen sol. to the following ODE

I solved the auxiliary eqn. for

So the roots must be complex? This is where I got stuck.

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- Mar 18th 2010, 10:26 PMmmattson07Higher Order ODE IVP
Hey MHF,

I got stuck on finding the gen sol. to the following ODE

I solved the auxiliary eqn. for

So the roots must be complex? This is where I got stuck. - Mar 18th 2010, 10:51 PMRandom Variable
The four roots are and

So the general solution is - Mar 19th 2010, 01:59 PMmmattson07
Ok so I can use that to solve the IVP.

so

and

so

Is this correct so far? - Mar 19th 2010, 02:17 PMRandom Variable
Are there any other conditions?

- Mar 19th 2010, 06:11 PMmmattson07
Yes but I figured since it only gets messier i'd make sure I got this much correct. The other conditions are:

and

I just do what I did above to find the constants? - Mar 19th 2010, 08:29 PMmmattson07
If what I did above is correct then

then

and

Idk if i'm on the right track here... - Mar 19th 2010, 09:14 PMRandom Variable
There is an error somewhere because the coefficients should be , and I'm not getting that by solving the four equations simultaneously.

- Mar 19th 2010, 09:50 PMmmattson07
I know y' is correct, I will double check y'' and y'''. Those roots make all four equations true though, how did you find them without solving the four equations simultaneously? Thanks.

- Mar 19th 2010, 09:57 PMRandom Variable
- Mar 19th 2010, 10:45 PMRandom Variable

EDIT:

which when solved, gives - Mar 20th 2010, 01:02 PMmmattson07
Your y'' matches the one I have above. However isn't sin(0)=0? So the C1 and C3 terms would go away when evaluated at 0? Leaving:

? - Mar 20th 2010, 01:09 PMRandom Variable
- Mar 20th 2010, 01:59 PMmmattson07
Ok so I had the last sign on y''' wrong yours was correct though. So we have

How do you deduct the constants from these? The only thing I could see is that

- Mar 20th 2010, 02:23 PMRandom Variable
From the first equation we also know that

Then from the second equation (1)

And from the fourth equation or (2)

Add (1) and (2) to get

so which means that

and going back to (1),

so which means that - Mar 20th 2010, 02:46 PMmmattson07
Ahh, and you can add those because they're both equal to 1?

And the solution to the IVP is