1. plz Help me

what is y?
$\displaystyle y^(5)+2y=0$

2. Originally Posted by iloveyou7
what is y?
$\displaystyle y^(5)+2y=0$

I'm not sure I understand. Is this the equation:

$\displaystyle y^5 + 2y = 0$?

You've posted this in the differential equation section, and this isn't a differential equation. Did you mean:

$\displaystyle \frac{d^5y}{dx^5} + 2y = 0$?

3. Originally Posted by Mush
I'm not sure I understand. Is this the equation:

$\displaystyle y^5 + 2y = 0$?

You've posted this in the differential equation section, and this isn't a differential equation. Did you mean:

$\displaystyle \frac{d^5y}{dx^5} + 2y = 0$?
yes, i mean
$\displaystyle \frac{d^5y}{dx^5} + 2y = 0$

4. Originally Posted by iloveyou7
what is y?
$\displaystyle y^{(5)}+2y=0$
Use a trial solution $\displaystyle e^{\lambda t}$ , this gives you a charateristic equation:

$\displaystyle \lambda^5+2=0$

so $\displaystyle \lambda=(-2)^{1/5}$ that is the general solution is:

$\displaystyle y(t)=Ae^{\lambda_1t}+Be^{\lambda_2t}+Ce^{\lambda_3 t}+De^{\lambda_4t}+Ee^{\lambda_5t}$

where the $\displaystyle \lambda_i$'s are the fith roots of $\displaystyle -2$

CB