plz Help me

**iloveyou7** · October 26th 2009, 05:39 AM

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

**Mush** · October 26th 2009, 06:00 AM

Originally Posted by iloveyou7

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

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

$y^5 + 2y = 0$ ?

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

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

**iloveyou7** · October 26th 2009, 06:38 AM

Originally Posted by Mush

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

$y^5 + 2y = 0$ ?

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

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

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

**CaptainBlack** · October 26th 2009, 07:40 AM

Originally Posted by iloveyou7

what is y?
$y^{(5)}+2y=0$

Use a trial solution $e^{\lambda t}$ , this gives you a charateristic equation:

$\lambda^5+2=0$

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

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

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

CB

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