# Thread: [SOLVED] need help on homogeneous ODE

1. ## [SOLVED] need help on homogeneous ODE

Hi can someone help me on this eqn..Btw im new here..cheers

y''''-4y'''+7y''-6y'+2y=0

It is to find the general solution..

2. Originally Posted by ashes
Hi can someone help me on this eqn..Btw im new here..cheers

y''''-4y'''+7y''-6y'+2y=0

It is to find the general solution..
This is a linear constant coefficient homogeneous ODE, so:

First solve the charateristic equation:

$\lambda^4-4 \lambda^3+7\lambda^2-6\lambda+2=0$

The roots of this are $\lambda=1$ (with multiplicity 2) and $\lambda=1 \pm i$, and your notes should tell you where to go from here.

RonL

3. therefore the r=1(with multiplicity 2) is actually a double root not a distinct root right?

4. Originally Posted by ashes
therefore the r=1(with multiplicity 2) is actually a double root not a distinct root right?

yes

RonL

5. ## differential eq

some help on solving this homogeneous ODE pls..

y''''+4k^4y=0 where k is non zero constant

6. Originally Posted by ashes
some help on solving this homogeneous ODE pls..

y''''+4k^4y=0 where k is non zero constant
Here the charateristic equation is:

$\lambda^4+4k^4=0$

or:

$\lambda^4=-4k^4=4k^4 e^{\pi i+2n\pi i}\ n=0,\ \pm 1,\ \pm2, ..$

so:

$\lambda = |k|\sqrt{2}~e^{\pi i/4+n\pi i/2},\ n=0, \ \pm 1,\ \pm2, ...$

and you will get four distinct values for $\lambda$ for $n=0, \ 1,\ 2,\ 3$

and the rest follows.

RonL

7. Originally Posted by ashes
some help on solving this homogeneous ODE pls..

y''''+4k^4y=0 where k is non zero constant
In future post new questions into new threads, that way we can see that
they need attention, and will probably be answered sooner.

RonL