Diff

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May 12th 2008, 11:59 AM
mladen

Diff

need help solving this diff plz

3y´ - y = 5x
May 12th 2008, 12:16 PM
nugiboy

I may be wrong, but i don't think you can solve that because there is only one equation and two unknowns.
May 12th 2008, 12:40 PM
Moo

Quote:

Originally Posted by nugiboy

I may be wrong, but i don't think you can solve that because there is only one equation and two unknowns.

It's a differential equation :)

y is a function of x
May 12th 2008, 12:50 PM
nugiboy

Quote:

Originally Posted by Moo

It's a differential equation :)

y is a function of x

How do you do it then lol?
May 13th 2008, 10:06 AM
mladen

Hello again, yes I know its a diff equation but I would need some guidence and help solving it =).

thank you
May 13th 2008, 11:19 AM
topsquark

Quote:

Originally Posted by mladen

need help solving this diff plz

3y´ - y = 5x

You can use an integrating factor:

First
$y' - \frac{1}{3}y = \frac{5}{3}x$

Then
$M(x) = e^{\int(-dx/3)} = e^{-x/3}$

So
$e^{-x/3}y' - \frac{1}{3}e^{-x/3}y = \frac{5}{3}xe^{-x/3}$

Notice that the left hand side of the equation is a "perfect derivative"
$\frac{d}{dx} \left ( e^{-x/3}y \right ) = \frac{5}{3}xe^{-x/3}$

$e^{-x/3}y = \int \frac{5}{3}xe^{-x/3}~dx$

I'll let you finish out from there.

-Dan

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