need help solving this diff plz

3y´ - y = 5x

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- May 12th 2008, 11:59 AMmladenDiff
need help solving this diff plz

3y´ - y = 5x - May 12th 2008, 12:16 PMnugiboy
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 PMMoo
- May 12th 2008, 12:50 PMnugiboy
- May 13th 2008, 10:06 AMmladen
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 AMtopsquark
You can use an integrating factor:

First

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

Then

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

So

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

Notice that the left hand side of the equation is a "perfect derivative"

$\displaystyle \frac{d}{dx} \left ( e^{-x/3}y \right ) = \frac{5}{3}xe^{-x/3}$

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

I'll let you finish out from there.

-Dan