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:
$\displaystyle \lambda^4-4 \lambda^3+7\lambda^2-6\lambda+2=0 $
The roots of this are $\displaystyle \lambda=1$ (with multiplicity 2) and $\displaystyle \lambda=1 \pm i $, and your notes should tell you where to go from here.
RonL
Here the charateristic equation is:
$\displaystyle \lambda^4+4k^4=0$
or:
$\displaystyle \lambda^4=-4k^4=4k^4 e^{\pi i+2n\pi i}\ n=0,\ \pm 1,\ \pm2, ..$
so:
$\displaystyle \lambda = |k|\sqrt{2}~e^{\pi i/4+n\pi i/2},\ n=0, \ \pm 1,\ \pm2, ...$
and you will get four distinct values for $\displaystyle \lambda$ for $\displaystyle n=0, \ 1,\ 2,\ 3$
and the rest follows.
RonL